The paper proves q-analogues of long-cycle factorization generating functions in the Hecke algebra, with q-Catalan, q-Narayana, and q-binomial specializations.
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.
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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.