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math.RT2025
A basis and Schur-Weyl duality for the loop Hecke algebra
Geoffrey Janssens, Abel Lacabanne, Léo Schelstraete +1
The loop Hecke algebra is a generalization of the Hecke algebra to the loop braid group, introduced by Damiani, Martin and Rowell. We give a new presentation of the loop Hecke alge…
math.RT2024
On Hecke and asymptotic categories for a family of complex reflection groups
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
Generalizing the dihedral picture for G(M,M,2), we construct Hecke algebras (and present a strategy for constructing Hecke categories) and asymptotic counterparts. We think of thes…
math.RT2020
Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras
Abel Lacabanne, Pedro Vaz
We prove a Schur-Weyl duality between the quantum enveloping algebra of and certain quotient algebras of Ariki-Koike algebras, which we give explicitly. The duali…