Tensor products on quiver representations

Quiver Varieties and Tensor Products

In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety Z̃ in a quiver variety, and show the following results: (1) The homology group of Z̃ is a representation of a symmetric Kac-Moody Lie algebra g, isomorphic to the tensor product V (λ1)⊗· · ·⊗V (λN ) of integrable highest weight modu...

On Tensor Products of Polynomial Representations

We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of GL(n, C) is isomorphic to another. As a consequence we discover families of LittlewoodRichardson coefficients that are non-zero, and a condition on Schur non-negativity.

Tensor Products of Level Zero Representations

In this paper we give a sufficient condition for the tensor product of irreducible finite–dimensional representations of quantum affine algebras to be cyclic. In particular, this proves a generalization of a recent result of Kashiwara [K], and also establishes a conjecture stated in that paper. We describe our results in some detail. Let g be a complex simple finite– dimensional Lie algebra of ...

On Tensor Products of Modular Representations of Symmetric Groups

Cluster Algebras and Quiver Representations

These notes contain an extended abstract and references for a minicourse given at the Summer School ‘Microlocal and Geometric Methods in Representation Theory’ (Schloss Reisensburg, July 2006) of the International Research Training Group Metz–Paderborn.