Modular Harish-Chandra series, Hecke algebras and (generalized) q-Schur algebras

2012 ◽  
pp. 1-66 ◽  
Author(s):  
Meinolf Geek
Keyword(s):  
Hecke Algebras ◽  
Schur Algebras

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 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.

STRATIFYING SYSTEMS, FILTRATION MULTIPLICITIES AND SYMMETRIC GROUPS

2005 ◽  
Vol 04 (05) ◽  
pp. 551-555 ◽  
Author(s):  
KARIN ERDMANN
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Schur Algebras

We show that the theorem by Hemmer and Nakano, on uniqueness of Specht filtration multiplicities, can be proved working entirely with representations of symmetric groups, or Hecke algebras. Furthermore, we give a new proof that Schur algebras are quasi-hereditary provided the characteristic of the field is at least 5. Our tools are some more general results on stratifying systems.

Cyclotomic Schur Algebras and Blocks of Cyclic Defect

2000 ◽  
Vol 43 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Steffen König
Keyword(s):  
Hecke Algebras ◽  
Schur Algebras ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Cyclotomic Hecke Algebras

AbstractAn explicit classification is given of blocks of cyclic defect of cyclotomic Schur algebras and of cyclotomic Hecke algebras, over discrete valuation rings.

scholarly journals q-SCHUR ALGEBRAS CORRESPONDING TO HECKE ALGEBRAS OF TYPE B

2020 ◽  
Author(s):  
CHUN-JU LAI ◽  
DANIEL K. NAKANO ◽  
ZIQING XIANG
Keyword(s):  
Hecke Algebras ◽  
Type B ◽  
Schur Algebras

Standardly based algebras and 0-Hecke algebras

2015 ◽  
Vol 14 (10) ◽  
pp. 1550141 ◽  
Author(s):  
Guiyu Yang ◽  
Yanbo Li
Keyword(s):  
Hecke Algebras ◽  
Hecke Algebra ◽  
Point Of View ◽  
Schur Algebras ◽  
Simple Modules

In this paper we prove that standardly based algebras are invariant under Morita equivalences. As an application, we prove 0-Hecke algebras and 0-Schur algebras are standardly based algebras. From this point of view, we give a new way to construct the simple modules of 0-Hecke algebras, and prove that the dimension of the center of a symmetric 0-Hecke algebra is not less than the number of its simple modules.

Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

2004 ◽  
Vol 7 (1) ◽  
pp. 67-99 ◽  
Author(s):  
Stephen R. Doty ◽  
Karin Erdmann ◽  
Daniel K. Nakano
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Schur Algebras
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