Dimensions of components of tensor products of representations of linear groups with applications to Beurling–Fourier algebras
Volume 220 / 2014
Studia Mathematica 220 (2014), 221-241
MSC: Primary 05E10; Secondary 22E46, 43A30, 47L30, 51F25.
DOI: 10.4064/sm220-3-2
Abstract
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of representations of the linear group $\operatorname{GL} (n)$ and universal upper bounds on the relative dimensions of irreducible components of a tensor product of representations of the special linear group $\operatorname{SL} (n)$. This problem is motivated by harmonic analysis problems, and we give some applications to the theory of Beurling–Fourier algebras.
