Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group

1999 ◽  
Author(s):  
Andrew Mathas
Keyword(s):  
Symmetric Group ◽  
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 On bases of centres of Iwahori–Hecke algebras of the symmetric group

2005 ◽  
Vol 289 (1) ◽  
pp. 42-69 ◽  
Author(s):  
Andrew Francis ◽  
Lenny Jones
Keyword(s):  
Symmetric Group ◽  
Hecke Algebras

scholarly journals Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)

1998 ◽  
Vol 50 (1) ◽  
pp. 167-192 ◽  
Author(s):  
Tom Halverson ◽  
Arun Ram
Keyword(s):  
Symmetric Group ◽  
Infinite Series ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Diagonal Matrix ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Irreducible Characters ◽  
Complex Reflection ◽  
Complex Reflection Groups

AbstractIwahori-Hecke algebras for the infinite series of complex reflection groups G(r, p, n) were constructed recently in the work of Ariki and Koike [AK], Broué andMalle [BM], and Ariki [Ari]. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper [HR] in whichwe derivedMurnaghan-Nakayama rules for the characters of the Iwahori-Hecke algebras of the classical Weyl groups. In both papers we have been motivated by C. Greene [Gre], who gave a new derivation of the Murnaghan-Nakayama formula for irreducible symmetric group characters by summing diagonal matrix entries in Young's seminormal representations. We use the analogous representations of the Iwahori-Hecke algebra of G(r, p, n) given by Ariki and Koike [AK] and Ariki [Ari].

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.

Some decomposition numbers for Hecke algebras of general linear groups

1996 ◽  
Vol 119 (3) ◽  
pp. 383-402 ◽  
Author(s):  
Matthew J. Richards
Keyword(s):  
Symmetric Group ◽  
Recent Work ◽  
Hecke Algebras ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Decomposition Numbers ◽  
Weight One

The theorem which is still known as Nakayama's Conjecture shows how the modular characters of the symmetric group Sn can be divided into blocks of various weights, those with the same weight having similar properties. In fact, all blocks of weight one have essentially the same decomposition numbers and these are easy to describe. In recent work, Scopes [16, 17] has shown that there are essentially only finitely many possibilities for the decomposition numbers for blocks of any given weight, and has given a bound for the number. We develop the combinatorics implicit in her work, and so establish an improved bound.

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.

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