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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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Collins B., Lee H., Śniady P.

Studia Mathematica

2014

tom 220

nr 3

221-241

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.

Quantum permutation groups: a survey

100%

Banica T., Bichon J., Collins B.

Banach Center Publications

2007

tom 78

nr 1

13-34

This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic laws, matrix models; the hyperoctahedral quantum group, free wreath products, quantum automorphism groups of finite graphs, graphs having no quantum symmetry; complex Hadamard matrices, cocycle twists of the symmetric group, quantum groups acting on 4 points; remarks and comments.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Collins B.

1 Banica T.

1 Bichon J.

1 Lee H.

1 Śniady P.

1 2014

1 2007

Wyniki wyszukiwania

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

Quantum permutation groups: a survey