Representations of and and the q-Schur algebra
Representations of the generalized symmetric groups.
Robinson-Schensted correspondence for the signed Brauer algebras.
RSK bases and Kazhdan-Lusztig cells
From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, “ RSK bases” are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory, both ordinary and modular, of the symmetric group are discussed.
Schubert and Grothendieck: a bidecennial balance. (Schubert et Grothendieck: un bilan bidécennal.)
Semilinear Automorphisms and Dimension Functions for Certain Characters of Finite Chevalley Groups.
Some problems in number theory that arise from group theory.
In this expository paper, we present several open problerns in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Specht modules for finite groups
Specht modules for Weyl groups.
Speciation: A case study in symmetric bifurcation theory.
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
Symmetric and antisymmetric vector-valued Jack polynomials.
Symmetry classes of tensors associated with the semi-dihedral groups
We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups . In particular, a necessary and sufficient condition for the existence of such a basis associated with and degree two characters is given.
Tableaux de Young et fonctions de Schur-Littlewood
Tensor Products and Dimensions of simple Modules for Symmetric Groups.
The action of the symmetric group on a generalized partition semilattice.
The actions of Sn+1 and Sn on the cohomology ring of a Coxeter arrangement of type An-1.
The Alperin-McKay conjecture holds in the covering groups of symmetric and alternating groups, p ... 2.
The Blocks of Finite General Linear and Unitary Groups.
The characters of a group of type .