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

Tom 220 / 2014

Benoît Collins, Hun Hee Lee, Piotr Śniady Studia Mathematica 220 (2014), 221-241 MSC: Primary 05E10; Secondary 22E46, 43A30, 47L30, 51F25. DOI: 10.4064/sm220-3-2

Streszczenie

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.

Autorzy

  • Benoît CollinsDépartement de Mathématique et Statistique
    Université d'Ottawa
    585 King Edward
    Ottawa, ON, K1N6N5 Canada
    and
    WPI-AIMR, Tohoku University
    Mathematics Unit
    Sendai, Japan
    and
    CNRS, Institut Camille Jordan Université Lyon 1
    43 Bd du 11 Novembre 1918
    69622 Villeurbanne, France
    e-mail
  • Hun Hee LeeDepartment of Mathematical Sciences
    Seoul National University
    Seoul 151-747, Republic of Korea
    e-mail
  • Piotr ŚniadyZentrum Mathematik, M5
    Technische Universität München
    Boltzmannstrasse 3
    85748 Garching, Germany
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    and
    Institute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
    e-mail

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