scholarly journals Another runner removal theorem for v-decomposition numbers of Iwahori–Hecke algebras and q-Schur algebras

2007 ◽  
Vol 310 (1) ◽  
pp. 396-404 ◽  
Author(s):  
Matthew Fayers
Keyword(s):  
Hecke Algebras ◽  
Schur Algebras ◽  
Decomposition Numbers

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

scholarly journals Some Decomposition Numbers of Hecke Algebras

1997 ◽  
Vol 187 (2) ◽  
pp. 493-509 ◽  
Author(s):  
C.A. Pallikaros
Keyword(s):  
Hecke Algebras ◽  
Decomposition Numbers

scholarly journals Schur Algebras and Quantum Symmetric Pairs With Unequal Parameters

2019 ◽  
Author(s):  
Chun-Ju Lai ◽  
Li Luo
Keyword(s):  
Weight Function ◽  
Canonical Basis ◽  
Hecke Algebras ◽  
Symmetric Pair ◽  
Type B ◽  
Schur Algebras ◽  
Algebraic Version ◽  
Type D ◽  
Invariant Basis

Abstract We study the (quantum) Schur algebras of type B/C corresponding to the Hecke algebras with unequal parameters. We prove that the Schur algebras afford a stabilization construction in the sense of Beilinson–Lusztig–MacPherson that constructs a multiparameter upgrade of the quantum symmetric pair coideal subalgebras of type AIII/AIV with no black nodes. We further obtain the canonical basis of the Schur/coideal subalgebras, at the specialization associated with any weight function. These bases are the counterparts of Lusztig’s bar-invariant basis for Hecke algebras with unequal parameters. In the appendix we provide an algebraic version of a type D Beilinson–Lusztig–MacPherson construction, which is first introduced by Fan–Li from a geometric viewpoint.

scholarly journals Graded decomposition numbers for cyclotomic Hecke algebras

2009 ◽  
Vol 222 (6) ◽  
pp. 1883-1942 ◽  
Author(s):  
Jonathan Brundan ◽  
Alexander Kleshchev
Keyword(s):  
Hecke Algebras ◽  
Decomposition Numbers ◽  
Cyclotomic Hecke Algebras
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