Categorical diagonalization of full twists

Ben Elias; Matthew Hogancamp

Categorical diagonalization of full twists

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arxiv 1801.00191 v2 pith:JXOLNKXB submitted 2017-12-30 math.RT math.GTmath.QA

Ben Elias , Matthew Hogancamp This is my paper · ORCID

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keywords categoricalconjecturediagonalizationfullassociatedauthorsbimodulesbraid

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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.

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Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
math.CO 2025-06 accept novelty 7.0 of 10

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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