We present a fast algorithm for computing the global crystal basis of the basic U_q (sl _n)-
module. This algorithm is based on combinatorial techniques which have been developed …

The representation theory of symmetric groups is one of the most beautiful, popular, and
important parts of algebra with many deep relations to other areas of mathematics, such as …

In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic
Hecke algebras. In this article, we prove a graded version of the Lascoux–Leclerc–Thibon …

Let S d denote the symmetric group on d letters. In 1979 Mullineux conjectured a
combinatorial algorithm for calculating the effect of tensoring with an irreducible S d-module …

The representation theory of finite groups has, at its core, a collection of open problems.
Taken together, they are called 'local-global conjectures', although 'localglobal rough …

We prove the quantum version-for Hecke algebras at roots of unity-of Kleshchev's modular
branching rule for symmetric groups. This result describes the socle of the restriction of an …

We survey some fundamental trends in representation theory of symmetric groups and
related objects which became apparent in the last fifteen years. The emphasis is on …

A Chevalley type integral basis for the ortho‐symplectic Lie superalgebra is constructed. The
simple modules of the ortho‐symplectic supergroup over an algebraically closed field of …

This paper is concerned with properties of the Mullineux map, which plays a rôle in p-
modular representation theory of symmetric groups. We introduce the residue symbol for a p …

In this paper we find the multiplicities. We provide different bases of the corresponding
weight spaces and outline some applications to the symmetric groups. In particular we …