On tensor products of irreducible integrable 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.

Irreducible Tensor Products over Alternating Groups

Unique Decomposition of Tensor Products of Irreducible Representations of Simple Algebraic Groups

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers.

Irreducible Decomposition for Tensor Product Representations of Jordanian Quantum Algebras

Tensor products of irreducible representations of the Jordanian quantum algebras Uh(sl(2)) and Uh(su(1, 1)) are considered. For both the highest weight finite dimensional representations of Uh(sl(2)) and lowest weight infinite dimensional ones of Uh(su(1, 1)) , it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exact...

Two-wavelet constants for square integrable representations of G/H

In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations fo...