相关论文: Restricting Specht modules of cyclotomic Hecke alg…

The reducibility of the Specht modules for the Iwahori--Hecke algebras in type $A$ is still open in the case where the defining parameter $q$ equals -1. We prove the reducibility of a large class of Specht modules for these algebras.

We give explicit isomorphisms between simple modules of degenerate cyclotomic Hecke algebras defined via various cellular bases. A special case gives a generalized Mullineux involution in the degenerate case.

Kleshchev, Mathas and Ram (2012) gave a presentation for graded Specht modules over Khovanov-Lauda-Rouquier algebras of finite and affine type A. We show that this construction can be applied more generally to skew shapes to give a…

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 this paper we study the partial Brauer $\mathbb{C}$-algebras $\mathfrak{R}_n(\delta,\delta')$, where $n \in \mathbb{N}$ and $\delta,\delta'\in\mathbb{C}$. We show that these algebras are generically semisimple, construct the Specht…

The graded Specht module $S^\lambda$ for a cyclotomic Hecke algebra comes with a distinguished generating vector $z^\lambda\in S^\lambda$, which can be thought of as a "highest weight vector of weight $\lambda$". This paper describes the…

We consider the problem of classifying irreducible Specht modules for the Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem completely in the case where q is not a root of unity, and in the case q=-1 we reduce the…

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…

We use a unified method to give an isomorphism between direct sums of cyclotomic affine (and degenerate affine) Hecke algebras and cyclotomic BK-subalgebras which are some KLR-type algebras.

We give a full classification, in terms of periodic skew diagrams, of irreducible semisimple modules in category O for the degenerate double affine Hecke algebra of type A which can be realized as submodules of Verma modules.

In this paper, we define a number of closely related isomorphisms. On one side of these isomorphisms sit a number of of algebras generalizing the Hecke and affine Hecke algebras, which we call the "Hecke family"; on the other, we find…

The reducible Specht modules for the Hecke algebra $\mathcal{H}_{\mathbb{F},q}(\mathfrak{S}_n)$ have been classified except when $q=-1$. We prove one half of a conjecture which we believe classifies the reducible Specht modules when $q=-1$…

We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type A. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we…

We clarify the links between the graded Specht construction of modules over cyclotomic Hecke algebras and the RSK construction for quiver Hecke algebras of type A, that was recently imported from the setting of representations of p-adic…

According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant $K$-group of Steinberg's triple variety. The $K$-group is equipped with a filtration indexed by closed $G$-stable…

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…

We associate a monoidal category $\mathcal{H}^\lambda$ to each dominant integral weight $\lambda$ of $\widehat{\mathfrak{sl}}_p$ or $\mathfrak{sl}_\infty$. These categories, defined in terms of planar diagrams, act naturally on categories…

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 $H_{\mathbf{k}}$ be a symplectic reflection algebra corresponding to a cyclic subgroup $\Gamma \subseteq SL_2 \C$ of order $n$ and $U_{\mathbf{k}} = eH_{\mathbf{k}} e$ the spherical subalgebra of $H_{\mathbf{k}}$. We show that for…

The paper studies the modular representation theory of the cyclotomic Hecke algebras of type $G(r,p,n)$ with $(\eps,q)$-separated parameters. We show that the decomposition numbers of these algebras are completely determined by the…