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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 4, Pages 98–104 (Mi faa2927)  

This article is cited in 2 scientific papers (total in 2 papers)

Discrete Series of Representations for the Modular Double of the Quantum Group $U_q(\operatorname{sl}(2,\mathbb{R}))$

L. D. Faddeev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The modular double of the quantum group $U_q(\operatorname{sl}(2))$ with deformation parameter $q=e^{i\pi\tau}$ is a natural object explicitly taking into account the duality $\tau\mapsto 1/\tau$. The use of the modular double in conformal field theory allows one to consider the region $1<c<25$ for the central charge of the Virasoro algebra when $|\tau|=1$. In this paper, a new discrete series of representations for the modular double of $U_q(\operatorname{sl}(2,\mathbb{R}))$ is found for such $\tau$.

Keywords: representation theory, quantum group, modular double

DOI: https://doi.org/10.4213/faa2927

Full text: PDF file (153 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:4, 330–335

Bibliographic databases:

UDC: 517.98+512.54
Received: 28.05.2008

Citation: L. D. Faddeev, “Discrete Series of Representations for the Modular Double of the Quantum Group $U_q(\operatorname{sl}(2,\mathbb{R}))$”, Funktsional. Anal. i Prilozhen., 42:4 (2008), 98–104; Funct. Anal. Appl., 42:4 (2008), 330–335

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. È. Derkachev, V. P. Spiridonov, “Finite-dimensional representations of the elliptic modular double”, Theoret. and Math. Phys., 183:2 (2015), 597–618  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Russian Math. Surveys, 72:6 (2017), 977–1081  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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