scholarly journals Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras

2012 ◽  
pp. 77-89 ◽  
Author(s):  
Maria Chlouveraki ◽  
Iain Gordon ◽  
Stephen Griffeth
Keyword(s):  
Hecke Algebras ◽  
Cherednik Algebras ◽  
Cell Modules ◽  
Basic Sets

scholarly journals SCHUR ELEMENTS AND BASIC SETS FOR CYCLOTOMIC HECKE ALGEBRAS

2011 ◽  
Vol 10 (05) ◽  
pp. 979-993 ◽  
Author(s):  
MARIA CHLOUVERAKI ◽  
NICOLAS JACON
Keyword(s):  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Schur Elements ◽  
Basic Sets ◽  
Cyclotomic Hecke Algebras

We study the Schur elements and the a-function for cyclotomic Hecke algebras. As a consequence, we show the existence of canonical basic sets, as defined by Geck–Rouquier, for certain complex reflection groups. This includes the case of finite Weyl groups for all choices of parameters (in characteristic 0).

scholarly journals DIAGRAM ALGEBRAS, DOMINANCE TRIANGULARITY AND SKEW CELL MODULES

2017 ◽  
Vol 104 (1) ◽  
pp. 13-36 ◽  
Author(s):  
CHRISTOPHER BOWMAN ◽  
JOHN ENYANG ◽  
FREDERICK GOODMAN
Keyword(s):  
Transition Matrix ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Specht Modules ◽  
Diagram Algebras ◽  
Cell Modules ◽  
Abstract Framework

We present an abstract framework for the axiomatic study of diagram algebras. Algebras that fit this framework possess analogues of both the Murphy and seminormal bases of the Hecke algebras of the symmetric groups. We show that the transition matrix between these bases is dominance unitriangular. We construct analogues of the skew Specht modules in this setting. This allows us to propose a natural tableaux theoretic framework in which to study the infamous Kronecker problem.

scholarly journals Decomposition matrices for d-Harish-Chandra series: the exceptional rank two cases

2011 ◽  
Vol 14 ◽  
pp. 271-290 ◽  
Author(s):  
Maria Chlouveraki ◽  
Hyohe Miyachi
Keyword(s):  
Characteristic Zero ◽  
Hecke Algebras ◽  
Irreducible Representations ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Basic Sets ◽  
Cyclotomic Hecke Algebras

AbstractWe calculate all decomposition matrices of the cyclotomic Hecke algebras of the rank two exceptional complex reflection groups in characteristic zero. We prove the existence of canonical basic sets in the sense of Geck–Rouquier and show that all modular irreducible representations can be lifted to the ordinary ones.

scholarly journals Cell 2-representations of finitary 2-categories

2011 ◽  
Vol 147 (5) ◽  
pp. 1519-1545 ◽  
Author(s):  
Volodymyr Mazorchuk ◽  
Vanessa Miemietz
Keyword(s):  
Hecke Algebras ◽  
Uniqueness Result ◽  
Verma Modules ◽  
Finite Dimensional ◽  
Cell Modules ◽  
Finite Dimensional Algebras

AbstractWe study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite-dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations inspired by Kazhdan–Lusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do not depend on the choice of a right cell inside a two-sided cell. This reproves and extends the uniqueness result on categorification of Kazhdan–Lusztig cell modules for Hecke algebras of type A from [V. Mazorchuk and C. Stroppel, Categorification of (induced) cell modules and the rough structure of generalised Verma modules, Adv. Math. 219 (2008), 1363–1426].

scholarly journals On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras

2022 ◽  
Vol 28 (2) ◽  
Author(s):  
C. Bowman ◽  
E. Norton ◽  
J. Simental
Keyword(s):  
Linear Subspace ◽  
Betti Numbers ◽  
Hecke Algebras ◽  
Simple Modules ◽  
Cherednik Algebras ◽  
Subspace Arrangements

AbstractWe provide a homological construction of unitary simple modules of Cherednik and Hecke algebras of type A via BGG resolutions, solving a conjecture of Berkesch–Griffeth–Sam. We vastly generalize the conjecture and its solution to cyclotomic Cherednik and Hecke algebras over arbitrary ground fields, and calculate the Betti numbers and Castelnuovo–Mumford regularity of certain symmetric linear subspace arrangements.

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