相关论文: Specht modules and Kazhdan--Lusztig cells in type …

A conjecture of C. Bonnaf\'e, M. Geck, L. Iancu, and T. Lam parameterizes Kazhdan-Lusztig left cells for unequal parameter Hecke algebras in type $B_n$ by families of standard domino tableaux of arbitrary rank. Relying on a family of…

Let $\cH$ be the one-parameter Hecke algebra associated to a finite Weyl group $W$, defined over a ground ring in which ``bad'' primes for $W$ are invertible. Using deep properties of the Kazhdan--Lusztig basis of $\cH$ and Lusztig's…

Let $H$ be the Iwahori--Hecke algebra associated with $S_n$, the symmetric group on $n$ symbols. This algebra has two important bases: the Kazhdan--Lusztig basis and the Murphy basis. While the former admits a deep geometric interpretation,…

Based on empirical evidence obtained using the {\sf CHEVIE} computer algebra system, we present a series of conjectures concerning the combinatorial description of the Kazhdan--Lusztig cells for type $B_n$ with unequal parameters. These…

We introduce cell modules for the tabular algebras defined in a previous work (math.QA/0107230); these modules are analogous to the representations arising from left Kazhdan--Lusztig cells. The standard modules of the title are constructed…

In this paper, we let $\Hecke$ be the Hecke algebra associated with a finite Coxeter group $W$ and with one-parameter, over the ring of scalars $\Alg=\mathbb{Z}(q, q^{-1})$. With an elementary method, we introduce a cellular basis of…

Using a characterization of a generalized $\tau$-invariant for intermediate parameter Hecke algebras in type $B_n$, we verify a conjectural description of Kazhdan-Lusztig cells in this setting due to C. Bonnaf\'e, L. Iancu, M. Geck, and T.…

More than 10 years ago, Dipper, James and Murphy developped the theory of Specht modules for Hecke algebras of type $B\_n$. More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrisations of the…

Let "$\leq_L$" be the Kazhdan-Lusztig left cell preorder on the symmetric group $S_n$. Let $w\mapsto (P(w),Q(w))$ be the Robinson-Schensted-Knuth correspondence between $S_n$ and the set of standard tableaux with the same shapes. We prove…

We show that the poset of alternating sign matrices, with Bruhat order, is isomorphic to the poset of certain submodules of the dominant Verma module for the special linear Lie algebra $\frak{sl}_n$. The latter poset consists of the…

Specht modules for an Ariki-Koike algebra have been investigated recently in the context of cellular algebras. Thus, these modules are defined as quotient modules of certain ``permutation'' modules, that is, defined as ``cell modules'' via…

In [14] Hemmer conjectures that the module of fixed points for the symmetric group $\Sigma_m$ of a Specht module for $\Sigma_n$ (with $n>m$), over a field of positive characteristic $p$, has a Specht series, when viewed as a…

Let $\H_n$ be a (degenerate or non-degenerate) Hecke algebra of type $G(\ell,1,n)$, defined over a commutative ring $R$ with one, and let $S(\bmu)$ be a Specht module for $\H_n$. This paper shows that the induced Specht module…

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…

The aim of this paper is to gather and (try to) unify several approaches for the modular representation theory of Hecke algebras of type $B$. We attempt to explain the connections between Geck's cellular structures (coming from…

The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group…

We 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…

Recently, the first two authors have defined a Z-grading on group algebras of symmetric groups and more generally on the cyclotomic Hecke algebras of type G(l,1,d). In this paper we explain how to grade Specht modules over these algebras.

Cohomology of Specht modules for the symmetric group can be equated in low degrees with corresponding cohomology for the Borel subgroup B of the general linear group GL_d(k), but this has never been exploited to prove new symmetric group…

We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Mili\v{c}i\'c-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra…