On Tensor Products of Polynomial Representations

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

Tensor Products of Holomorphic Representations and Bilinear Differential Operators

Let be weighted Bergman space on a bounded symmetric domain . It has analytic continuation in the weight and for in the so-called Wallach set still forms unitary irreducible (projective) representations of . We give the irreducible decomposition of the tensor product of the representation for any two unitary weights and we find the highest weight vectors of the irreducible components. We find a...

Determining summands in tensor products of Lie algebra representations

Aslaksen, H., Determining summands in tensor products of Lie algebra representations, Journal of Pure and Applied Algebra 93 (1994) 135-146. We give some results that enable us to find certain summands in tensor products of Lie algebra representations. We concentrate on the splitting of tensor squares into their symmetric and antisymmetric parts. Our results are valid for any Lie algebra of arb...