Paper Citation Record · LEDGER

Vogel's universality and Macdonald dimensions

As of 20 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 2 inbound Pith citation observations for arXiv:2507.11414.

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pith.paper-citation-record.v1
2507.11414 v2

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Source: arxiv_reference, observed 2026-05-18T23:56:55.504554Z

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Outbound references

Observation ede6e6c5-c253-4d0b-9afc-171dcff03c6b · outbound

This paper cites Vogel, Algebraic structures on modules of diagrams , Preprint (1995), available at https://webusers.

Vogel's universality and Macdonald dimensions Vogel, Algebraic structures on modules of diagrams , Preprint (1995), available at https://webusers

Reference 1

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Observation d4410afc-77b3-48e2-9049-c77d800e991a · outbound

This paper cites Vogel, The Universal Lie algebra , Preprint (1999), available at https://webusers.imj-prg.fr/ ~pierre.vogel/grenoble-99b.pdf.

Vogel's universality and Macdonald dimensions Vogel, The Universal Lie algebra , Preprint (1999), available at https://webusers.imj-prg.fr/ ~pierre.vogel/grenoble-99b.pdf

Reference 2

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Observation 616b1173-c807-45c7-bdf4-a80bc727905d · outbound

This paper cites Universality in Chern-Simons theory.

Vogel's universality and Macdonald dimensions Universality in Chern-Simons theory

Reference 3

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Observation 10489d34-d6fb-44f7-9d3d-ff14635fdfac · outbound

This paper cites Nonperturbative universal Chern-Simons theory.

Vogel's universality and Macdonald dimensions Nonperturbative universal Chern-Simons theory

Reference 4

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Observation 9c764760-2e7d-445b-a461-90851d4204a5 · outbound

This paper cites Exact Chern-Simons / Topological String duality.

Vogel's universality and Macdonald dimensions Exact Chern-Simons / Topological String duality

Reference 5

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Observation 1459dba0-60a0-4d69-92b4-853da535522b · outbound

This paper cites Partition function of Chern-Simons theory as renormalized q-dimension.

Vogel's universality and Macdonald dimensions Partition function of Chern-Simons theory as renormalized q-dimension

Reference 6

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Observation b2c07f18-8a8e-4b96-8cd8-88c8ad933ea5 · outbound

This paper cites Westbury, Proceedings of the Tenth Oporto Meeting on Geometry, Topology and Physics, 18 (2001) suppl.

Vogel's universality and Macdonald dimensions Westbury, Proceedings of the Tenth Oporto Meeting on Geometry, Topology and Physics, 18 (2001) suppl

Reference 7

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Observation 41bd320e-6535-410c-ab50-9dc3c3655177 · outbound

This paper cites On Universal Quantum Dimensions.

Vogel's universality and Macdonald dimensions On Universal Quantum Dimensions

Reference 8

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Observation f4f1cc63-272b-4dc0-b1b5-9c693a9dfc70 · outbound

This paper cites Landsberg, L.

Vogel's universality and Macdonald dimensions Landsberg, L

Reference 9

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Observation f579919e-55d2-4701-aa20-90619b8569e8 · outbound

This paper cites Casimir eigenvalues for universal Lie algebra.

Vogel's universality and Macdonald dimensions Casimir eigenvalues for universal Lie algebra

Reference 10

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Observation 4270bc3c-d0a5-4cea-b51f-b093b3b300cc · outbound

This paper cites The uniform structure of $\mathfrak{g}^{\otimes 4}$.

Vogel's universality and Macdonald dimensions The uniform structure of $\mathfrak{g}^{\otimes 4}$

Reference 11

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Observation bce5522a-50c6-4472-b6bb-b1d15bae5068 · outbound

This paper cites Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes 2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parametrization.

Vogel's universality and Macdonald dimensions Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes 2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parametrization

Reference 12

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Observation 190ed7ed-d9b1-4476-a8f9-da4767343545 · outbound

This paper cites Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations and Vogel parameters.

Vogel's universality and Macdonald dimensions Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations and Vogel parameters

Reference 13

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Observation 2c3ad023-d8ab-4c65-8989-56423310019f · outbound

This paper cites Split Casimir operator for simple Lie algebras in the cube of $\mathsf{ad}$-representation and Vogel parameters.

Vogel's universality and Macdonald dimensions Split Casimir operator for simple Lie algebras in the cube of $\mathsf{ad}$-representation and Vogel parameters

Reference 14

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Observation 5830813f-e72b-446e-ad4a-77fe67fc2701 · outbound

This paper cites Universal volume of groups and anomaly of Vogel's symmetry.

Vogel's universality and Macdonald dimensions Universal volume of groups and anomaly of Vogel's symmetry

Reference 15

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Observation 31d3ae85-d752-4046-9091-8568a0ec67a2 · outbound

This paper cites On universal knot polynomials.

Vogel's universality and Macdonald dimensions On universal knot polynomials

Reference 16

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Observation 8958c68d-8116-4c2d-8eb7-04bc5c229587 · outbound

This paper cites Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots.

Vogel's universality and Macdonald dimensions Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots

Reference 17

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Observation 65dd86f7-ed96-4fa9-9d8a-d018c8435616 · outbound

This paper cites Torus knots in adjoint representation and Vogel's universality.

Vogel's universality and Macdonald dimensions Torus knots in adjoint representation and Vogel's universality

Reference 18

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Observation e8bbfa6b-d27d-493e-8554-b9d3d3ede02c · outbound

This paper cites Construction of Lie algebra weight system kernel via Vogel algebra.

Vogel's universality and Macdonald dimensions Construction of Lie algebra weight system kernel via Vogel algebra

Reference 19

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Observation aab77b25-f1c2-4574-afcf-2a166fc6f7ce · outbound

This paper cites Knot Homology from Refined Chern-Simons Theory.

Vogel's universality and Macdonald dimensions Knot Homology from Refined Chern-Simons Theory

Reference 20

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Observation 357083a1-a919-4df4-a785-275ee107f243 · outbound

This paper cites Refined Chern-Simons Theory and Knot Homology.

Vogel's universality and Macdonald dimensions Refined Chern-Simons Theory and Knot Homology

Reference 21

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Observation 6ecd86ae-2711-4eb4-ad62-98ab4fbf4866 · outbound

This paper cites Refined Chern-Simons versus Vogel universality.

Vogel's universality and Macdonald dimensions Refined Chern-Simons versus Vogel universality

Reference 22

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Observation 3f0864e4-6948-4eda-82d2-0aecfc6ebd1a · outbound

This paper cites On partition functions of refined Chern-Simons theories on $S^3$.

Vogel's universality and Macdonald dimensions On partition functions of refined Chern-Simons theories on $S^3$

Reference 23

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Observation 303b5a5a-8c52-4a7d-b5e2-25ae2d8c603d · outbound

This paper cites Vogel's Universality and its Applications.

Vogel's universality and Macdonald dimensions Vogel's Universality and its Applications

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T17:22:33.001587Z

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Observation 38fe2ae6-8fff-4d37-a89b-2e3a1fd69ad0 · outbound

This paper cites Refined composite invariants of torus knots via DAHA.

Vogel's universality and Macdonald dimensions Refined composite invariants of torus knots via DAHA

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:22:36.295383Z

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Observation 06160fbb-57e5-469b-9c6c-7ae94aa28f3d · outbound

This paper cites Deligne, B.

Vogel's universality and Macdonald dimensions Deligne, B

Reference 26

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Observation 6b02fd64-bf77-4b99-b2f2-baff0fa29b24 · outbound

This paper cites On Refined Vogel's universality.

Vogel's universality and Macdonald dimensions On Refined Vogel's universality

Reference 27

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Observation 7a52c418-c885-41ce-b107-90d9987a946c · outbound

This paper cites Macdonald deformation of Vogel's universality and link hyperpolynomials.

Vogel's universality and Macdonald dimensions Macdonald deformation of Vogel's universality and link hyperpolynomials

Reference 28

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Observation 0ca0c287-3894-4e41-b7cf-df740f24cd44 · outbound

This paper cites Orthogonal polynomials associated with root systems.

Vogel's universality and Macdonald dimensions Orthogonal polynomials associated with root systems

Reference 29

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Observation 152a1f16-67d3-4878-b016-fa5b59289f4a · outbound

This paper cites Macdonald, SIAM J.Math.

Vogel's universality and Macdonald dimensions Macdonald, SIAM J.Math

Reference 30

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Observation e7d0c094-174f-4186-b187-f5297f75c228 · outbound

This paper cites Macdonald's Evaluation Conjectures and Difference Fourier Transform.

Vogel's universality and Macdonald dimensions Macdonald's Evaluation Conjectures and Difference Fourier Transform

Reference 31

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Observation d415bb14-7631-4185-9ee6-2a3c7b418458 · outbound

This paper cites Cherednik, The Annals of Mathematics, Second Series, 141 (1995) 191-216.

Vogel's universality and Macdonald dimensions Cherednik, The Annals of Mathematics, Second Series, 141 (1995) 191-216

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:22:37.983134Z

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Observation 0743fcdc-5240-4222-92e4-09be687cd249 · outbound

This paper cites Koornwinder, in: Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Appli- cations (Tampa, FL, 1991), Contemp.

Vogel's universality and Macdonald dimensions Koornwinder, in: Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Appli- cations (Tampa, FL, 1991), Contemp

Reference 33

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Observation f0c40bea-ac7f-4480-b192-29e2b2bd8a89 · outbound

This paper cites Macdonald, A new class of symmetric functions , Publ.I.R.M.A., Strasbourg, Actes 20-e Seminaire Lotharingen, (1988) 131-171.

Vogel's universality and Macdonald dimensions Macdonald, A new class of symmetric functions , Publ.I.R.M.A., Strasbourg, Actes 20-e Seminaire Lotharingen, (1988) 131-171

Reference 34

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Observation 4d75983f-57b8-45df-8d2d-e69c530a2773 · outbound

This paper cites Macdonald, Symmetric functions and Hall polynomials (2nd edition) , Clarendon Press, Oxford, 1995, 475 pp.

Vogel's universality and Macdonald dimensions Macdonald, Symmetric functions and Hall polynomials (2nd edition) , Clarendon Press, Oxford, 1995, 475 pp

Reference 35

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Observation c764cc44-5d7c-41d2-ae5c-ede326452202 · outbound

This paper cites Character Expansions for the Orthogonal and Symplectic Groups.

Vogel's universality and Macdonald dimensions Character Expansions for the Orthogonal and Symplectic Groups

Reference 36

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Vogel's universality and Macdonald dimensions Unresolved cited work

Reference 37

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Observation fae47ebe-a810-4592-ac42-47a4f732878b · outbound

This paper cites Di Francesco, P.

Vogel's universality and Macdonald dimensions Di Francesco, P

Reference 38

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Observation beb3a0d0-7e3f-4e3f-a889-9a2eab463b58 · outbound

This paper cites Uniqueness of universal dimensions and configurations of points and lines.

Vogel's universality and Macdonald dimensions Uniqueness of universal dimensions and configurations of points and lines

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:22:36.114544Z

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Observation 4a5f1cc1-da56-4c6b-8415-94fb57dd776c · outbound

This paper cites King, Can.

Vogel's universality and Macdonald dimensions King, Can

Reference 40

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Observation ac0a0785-8099-4fef-b0d2-7cefc41b0a07 · outbound

This paper cites Mkrtchyan, Phys.

Vogel's universality and Macdonald dimensions Mkrtchyan, Phys

Reference 41

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Observation 9b392774-250b-4168-856f-c453dcef34a7 · outbound

This paper cites Cvitanovic, Group Theory, Princeton Univ.

Vogel's universality and Macdonald dimensions Cvitanovic, Group Theory, Princeton Univ

Reference 42

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Observation ad65e5a3-a44c-4c96-9a3c-31f89829b330 · outbound

This paper cites On duality and negative dimensions in the theory of Lie groups and symmetric spaces.

Vogel's universality and Macdonald dimensions On duality and negative dimensions in the theory of Lie groups and symmetric spaces

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:22:35.911796Z

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Observation 6505145f-b225-4a86-aa52-4ec2dfa07cab · outbound

This paper cites Chern-Simons theory with the exceptional gauge group as a refined topological string.

Vogel's universality and Macdonald dimensions Chern-Simons theory with the exceptional gauge group as a refined topological string

Reference 44

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Observation 96d2bba8-6a6a-4e1b-b3df-dfd92829c980 · outbound

This paper cites On refined Chern-Simons / topological string duality for classical gauge groups.

Vogel's universality and Macdonald dimensions On refined Chern-Simons / topological string duality for classical gauge groups

Reference 45

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Observation 76a8d53e-b3a9-4653-9c8f-d9b52a06805e · outbound

This paper cites Two-fold refinement of non simply laced Chern-Simons theories.

Vogel's universality and Macdonald dimensions Two-fold refinement of non simply laced Chern-Simons theories

Reference 46

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Observation 7f01e340-e11a-4f70-8b85-40d842e76921 · outbound

This paper cites Refined $E_n$ Chern-Simons theory.

Vogel's universality and Macdonald dimensions Refined $E_n$ Chern-Simons theory

Reference 47

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Observation 451b3c96-0771-44b0-bec7-f5e1335780a3 · outbound

This paper cites Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$.

Vogel's universality and Macdonald dimensions Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$

Reference 48

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:22:35.718099Z

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Observation 68d88c98-2cc0-43f1-8c20-94253b578e85 · outbound

This paper cites Macdonald Polynomials of Type $C_n$ with One-Column Diagrams and Deformed Catalan Numbers.

Vogel's universality and Macdonald dimensions Macdonald Polynomials of Type $C_n$ with One-Column Diagrams and Deformed Catalan Numbers

Reference 49

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:22:35.575804Z

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Observation fc0c2ff0-2bd6-4fed-81b6-570907f599f3 · outbound

This paper cites BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials.

Vogel's universality and Macdonald dimensions BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials

Reference 50

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T17:22:35.416317Z

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Pith citing papers

Observation 22a17fb0-dcc7-4648-bb05-7c6d7693520e · inbound

Non-commutative creation operators for symmetric polynomials cites this paper.

Non-commutative creation operators for symmetric polynomials Vogel's universality and Macdonald dimensions

Reference 67

Resolution: verified exact; arxiv_id, observed 2026-05-18T23:56:55.508425Z

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Observation fcf7099d-ea3d-48c7-ad65-fa6db62d5bf1 · inbound

A note on universality in refined Chern-Simons theory cites this paper.

A note on universality in refined Chern-Simons theory Vogel's universality and Macdonald dimensions

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-13T03:47:12.775972Z

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