Geodesic
Dimensions of components of tensor products of representations of linear groups with applications to Beurling–Fourier algebras
Benoît Collins 1   ; Hun Hee Lee 2   ; Piotr Śniady 3
1 Département 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
2 Department of Mathematical Sciences Seoul National University Seoul 151-747, Republic of Korea
3 Zentrum 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
Studia Mathematica, Tome 220 (2014) no. 3, pp. 221-241 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\operatorname{GL} (n)$ 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.
DOI : 10.4064/sm220-3-2
Keywords: universal upper bounds relative dimensions isotypic components tensor product representations linear group operatorname universal upper bounds relative dimensions irreducible components tensor product representations special linear group operatorname problem motivated harmonic analysis problems applications theory beurling fourier algebras

Benoît Collins  1   ; Hun Hee Lee  2   ; Piotr Śniady  3

1 Département 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
2 Department of Mathematical Sciences Seoul National University Seoul 151-747, Republic of Korea
3 Zentrum 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 
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     title = {Dimensions of components of tensor products
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     doi = {10.4064/sm220-3-2},
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Benoît Collins; Hun Hee Lee; Piotr Śniady. Dimensions of components of tensor products
 of representations of linear groups
 with applications to Beurling–Fourier algebras. Studia Mathematica, Tome 220 (2014) no. 3, pp. 221-241. doi: 10.4064/sm220-3-2

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