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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 331, Pages 43–59
(Mi znsl249)
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This article is cited in 2 scientific papers (total in 2 papers)
The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions
E. E. Goryachko Saint-Petersburg State University
Abstract:
We consider the parabolic restriction of representations of
the group $GL(n+1,q)$ to the group $GL(n,q)$. The branching
of representations under this restriction is simple. We
present a direct proof of this fact in the case of the so-called
principal series representations. This statement is reduced to the
commutativity of the centralizer of the Hecke algebras
$Z(H(n,q),H(n+1,q))$; we prove it using an auxiliary
combinatorial theory.
Received: 25.05.2006
Citation:
E. E. Goryachko, “The simplicity of branching of the principal series representations of the groups $GL(n,q)$ under the parabolic restrictions”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Zap. Nauchn. Sem. POMI, 331, POMI, St. Petersburg, 2006, 43–59; J. Math. Sci. (N. Y.), 141:4 (2007), 1407–1416
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https://www.mathnet.ru/eng/znsl249 https://www.mathnet.ru/eng/znsl/v331/p43
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Abstract page: | 221 | Full-text PDF : | 52 | References: | 34 |
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