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Funktsional. Anal. i Prilozhen., 2010, Volume 44, Issue 2, Pages 92–96 (Mi faa2992)  

This article is cited in 7 scientific papers (total in 8 papers)

Brief communications

On holomorphic representations of discrete Heisenberg groups

A. N. Parshin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We define a class of monomial not necessary unitary representations of discrete Heisenberg groups. Their moduli space is a complex-analytic manifold. There exist characters of the representations which are automorphic forms on the moduli space.

Keywords: discrete Heisenberg group, induced representation, character, theta function

DOI: https://doi.org/10.4213/faa2992

Full text: PDF file (171 kB)
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English version:
Functional Analysis and Its Applications, 2010, 44:2, 156–159

Bibliographic databases:

Document Type: Article
UDC: 512.74
Received: 28.12.2009

Citation: A. N. Parshin, “On holomorphic representations of discrete Heisenberg groups”, Funktsional. Anal. i Prilozhen., 44:2 (2010), 92–96; Funct. Anal. Appl., 44:2 (2010), 156–159

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. Math., 75:4 (2011), 749–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818  mathnet  crossref  mathscinet  isi  elib  elib
    3. S. A. Arnal', A. N. Parshin, “On Irreducible Representations of Discrete Heisenberg Groups”, Math. Notes, 92:3 (2012), 295–301  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Liu D., “Theta functions and arithmetic quotients of loop groups”, Math. Res. Lett., 19:1 (2012), 13–29  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. R. Ya. Budylin, “Conjugacy classes in discrete Heisenberg groups”, Sb. Math., 205:8 (2014), 1069–1079  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. I. V. Beloshapka, S. O. Gorchinskiy, “Irreducible representations of finitely generated nilpotent groups”, Sb. Math., 207:1 (2016), 41–64  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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