This article is cited in 3 scientific papers (total in 3 papers)
Irreducible representations of finitely generated nilpotent groups
I. V. Beloshapkaa, S. O. Gorchinskiybc
a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c National Research University "Higher School of Economics" (HSE), Moscow
We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field.
Bibliography: 21 titles.
finitely generated nilpotent groups, monomial representations, finite weight representations.
|Russian Foundation for Basic Research
|Ministry of Education and Science of the Russian Federation
|This research was carried out with the support of the Russian
Foundation for Basic Research (grant no. 14-01-00178), the Programme
for the Support of Young Candidates of Science
(grant no. MK-5215.2015.1) and the Programme for the Support of Leading
Scientific Schools of the President of the Russian Federation (grant no. НШ-2998.2014.1).
The first author also acknowledges the support by RFBR grants no. 14-01-00160
and no. 13-01-00622. The second author acknowledges the support by
RFBR grant no. 13-01-12420, Dmitrii Zimin's “Dynasty”
Foundation and by the subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.
Author to whom correspondence should be addressed
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Sbornik: Mathematics, 2016, 207:1, 41–64
Received: 14.08.2015 and 28.09.2015
I. V. Beloshapka, S. O. Gorchinskiy, “Irreducible representations of finitely generated nilpotent groups”, Mat. Sb., 207:1 (2016), 45–72; Sb. Math., 207:1 (2016), 41–64
Citation in format AMSBIB
\by I.~V.~Beloshapka, S.~O.~Gorchinskiy
\paper Irreducible representations of finitely generated nilpotent groups
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
D. V. Osipov, A. N. Parshin, “Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201
E. K. Narayanan, P. Singla, “On monomial representations of finitely generated nilpotent groups”, Comm. Algebr., 46:6 (2018), 2319–2331
A. N. Parshin, “The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group”, Proc. Steklov Inst. Math., 307 (2019), 174–192
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