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1.
In this paper we investigate the left cell representations ofthe Iwahori-Hecke algebras associated to a finite Coxeter groupW. Our main result shows that , where w0 is the element of longest length in W, acts essentiallyas an involution upon the canonical bases of a cell representation.We describe some properties of this involution, use it to furtherdescribe the left cells, and finally show how to realize eachcell representation as a submodule of . Our results rely uponcertain positivity properties of the structure constants ofthe Kazhdan-Lusztig bases of the Hecke algebra and so have notyet been shown to apply to all finite Coxeter groups. 相似文献
2.
We prove a q-analogue of the Carter–Payne theorem in the case where the differences between the parts of the partitions are sufficiently
large. We identify a layer of the Jantzen filtration which contains the image of these Carter–Payne homomorphisms and we show
how these homomorphisms compose. 相似文献
3.
We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras
which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras
defined over fields of characteristic zero are now known in principle.
Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002 相似文献
4.
We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke algebras of type A and between the Weyl modules of the q-Schur algebra.This research was supported by ARC grant DP0343023. The first author was also supported by a Sesqui Research Fellowship at the University of Sydney. 相似文献
5.
Andrew Mathas 《中国科学 数学(英文版)》2018,61(2):299-310
This paper proves that the restriction of a Specht module for a (degenerate or non-degenerate) cyclotomic Hecke algebra, or KLR (Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration. 相似文献
6.
Andrew Mathas 《Journal of Algebraic Combinatorics》1999,9(3):295-313
In this paper we introduce a family of polynomials indexed by pairs of partitions and show that if these polynomials are self-orthogonal then the centre of the Iwahori-Hecke algebra of the symmetric group is precisely the set of symmetric polynomials in the Murphy operators. 相似文献
7.
This paper computes the irreducible characters of the alternating Hecke algebras, which are deformations of the group algebras of the alternating groups. More precisely, we compute the values of the irreducible characters of the semisimple alternating Hecke algebras on a set of elements indexed by minimal length conjugacy class representatives and we show that these character values determine the irreducible characters completely. As an application, we determine a splitting field for the alternating Hecke algebras in the semisimple case. 相似文献
8.
In this paper we use the Hecke algebra of type B to define anew algebra S which is an analogue of the q-Schur algebra. Weshow that S has generic basis which is independentof the choice of ring and the parameters q and Q. We then constructWeyl modules for S and obtain, as factor modules, a family ofirreducible S-modules defined over any field. 1991 MathematicsSubject Classification: 16G99, 20C20, 20G05. 相似文献
9.
This paper introduces an analogue of the Solomon descent algebra for the complex reflection groups of type G(r,1,n). As with the Solomon descent algebra, our algebra has a basis given by sums of ‘distinguished’ coset representatives for certain ‘reflection subgroups.’ We explicitly describe the structure constants with respect to this basis and show that they are polynomials in r. This allows us to define a deformation, or q-analogue, of these algebras which depends on a parameter q. We determine the irreducible representations of all of these algebras and give a basis for their radicals. Finally, we show that the direct sum of cyclotomic Solomon algebras is canonically isomorphic to a concatenation Hopf algebra. 相似文献
10.
Gordon James Andrew Mathas 《Transactions of the American Mathematical Society》2000,352(11):5381-5404
The cyclotomic -Schur algebra was introduced by Dipper, James and Mathas, in order to provide a new tool for studying the Ariki-Koike algebra. We here prove an analogue of Jantzen's sum formula for the cyclotomic -Schur algebra. Among the applications is a criterion for certain Specht modules of the Ariki-Koike algebras to be irreducible.