Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations

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...

Spectra of Tensor Products of Operators

Fluctuation Operators and Spontaneous Symmetry Breaking

In the following we develop an in various respects new approach to this field, which was to a large extent developed by Verbeure et al. and which may complement their approach, which is largely based on a noncommutative central limit theorem. In contrast to that we deal directly with the limits of l-point truncated correlation functions and show that they typically vanish for l ≥ 3 provided tha...

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 ...