Weak Containment and Tensor Products of Group Representations.

Eberhard Kaniuth

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Dimensions of components of tensor products of representations of linear groups with applications to Beurling-Fourier algebras

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We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of representations of the linear group GL(n) and universal upper bounds on the relative dimensions of irreducible components of a tensor product of representations of the special linear group SL(n). This problem is motivated by harmonic analysis problems, and we give some applications to the theory of Beurling-Fourier algebras.