Pith. sign in

REVIEW 2 cited by

The MacMahon R-matrix

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1810.07676 v2 pith:CBRKEZV3 submitted 2018-10-17 hep-th math-phmath.MPmath.QAmath.RT

classification hep-thmath-phmath.MPmath.QAmath.RT
keywords macmahonmatrixalgebraproductrepresentationtensorwidehatacting
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters $q$, $t^{-1}$ and $\frac{t}{q}$. We construct the intertwining operator for a tensor product of the horizontal Fock representation and the vertical MacMahon representation and show that the intertwiners are permuted using the MacMahon $R$-matrix.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Super-Hamiltonians for super-Macdonald polynomials

    hep-th 2025-01 conditional novelty 6.0 of 10

    Explicit vertex-operator super-Hamiltonians are conjectured whose eigenfunctions are the super-Macdonald polynomials of earlier work.

  2. Gauge Origami and BPS/CFT correspondence

    hep-th 2025-02 conditional novelty 5.0 of 10

    The gauge origami partition function on C4 is realized as a correlation function of BPS qq-character operators, with D6 and D8 characters labeled by plane and solid partitions.

Pith tools