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

• Autorzy: Benoît Collins , Hun Hee Lee , Piotr Śniady
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L30: Abstract operator algebras on Hilbert spaces
• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 51F25: Orthogonal and unitary groups
• 22E46: Semisimple Lie groups and their representations
• 05E10: Combinatorial aspects of representation theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 220
• Numer: 3
• Strony: 221-241

Daty

wydano

2014

Twórcy

autor

Benoît Collins

• Département de Mathématique et Statistique, Université d'Ottawa, 585 King Edward, Ottawa, ON, K1N6N5 Canada
• WPI-AIMR, Tohoku University, Mathematics Unit, Sendai, Japan
• CNRS, Institut Camille Jordan Université Lyon 1, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne, France

autor

Hun Hee Lee

• Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea

autor

Piotr Śniady

• Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm220-3-2