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Categorical diagonalization of full twists
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abstract
We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced earlier by the authors. We prove our conjecture in type $A$, and as a result we obtain a categorification of the Young idempotents.
Forward citations
Cited by 2 Pith papers
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Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
The paper proves q-analogues of long-cycle factorization generating functions in the Hecke algebra, with q-Catalan, q-Narayana, and q-binomial specializations.
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Homology Groups and Categorical Diagonalization
Under a splitting assumption, the paper asserts that a chain complex's homology object is the categorified eigenvalue of that complex with the ground ring as eigenobject; the converse half of the assertion is false over Z.
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