RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2015, Volume 183, Number 2, Pages 177–201 (Mi tmf8817)  

This article is cited in 4 scientific papers (total in 4 papers)

Finite-dimensional representations of the elliptic modular double

S. È. Derkacheva, V. P. Spiridonovb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
b Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Dubna, Moscow Oblast, Russia

Abstract: We investigate the kernel space of an integral operator $\mathrm M(g)$ depending on the "spin" $g$ and describing an elliptic Fourier transformation. The operator $\mathrm M(g)$ is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with the parameters $\eta$ and $\tau$, $\operatorname{Im}\tau>0$, $\operatorname{Im}\eta>0$. For two-dimensional lattices $g=n\eta+m\tau/2$ and $g=1/2+n\eta+m\tau/2$ with incommensurate $1,2\eta,\tau$ and integers $n,m>0$, the operator $\mathrm M(g)$ has a finite-dimensional kernel that consists of the products of theta functions with two different modular parameters and is invariant under the action of generators of the elliptic modular double.

Keywords: Yang–Baxter equation, elliptic modular double, elliptic hypergeometric function

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12405
14-01-00341
11-01-00980
14-01-00474
National Research University Higher School of Economics 13-09-0133


DOI: https://doi.org/10.4213/tmf8817

Full text: PDF file (516 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2015, 183:2, 597–618

Bibliographic databases:

Received: 10.11.2014

Citation: S. È. Derkachev, V. P. Spiridonov, “Finite-dimensional representations of the elliptic modular double”, TMF, 183:2 (2015), 177–201; Theoret. and Math. Phys., 183:2 (2015), 597–618

Citation in format AMSBIB
\Bibitem{DerSpi15}
\by S.~\`E.~Derkachev, V.~P.~Spiridonov
\paper Finite-dimensional representations of the~elliptic modular double
\jour TMF
\yr 2015
\vol 183
\issue 2
\pages 177--201
\mathnet{http://mi.mathnet.ru/tmf8817}
\crossref{https://doi.org/10.4213/tmf8817}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3399641}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015TMP...183..597D}
\elib{https://elibrary.ru/item.asp?id=23421744}
\transl
\jour Theoret. and Math. Phys.
\yr 2015
\vol 183
\issue 2
\pages 597--618
\crossref{https://doi.org/10.1007/s11232-015-0284-0}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000355826000002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84930640049}


Linking options:
  • http://mi.mathnet.ru/eng/tmf8817
  • https://doi.org/10.4213/tmf8817
  • http://mi.mathnet.ru/eng/tmf/v183/i2/p177

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav P. Spiridonov, “From Principal Series to Finite-Dimensional Solutions of the Yang–Baxter Equation”, SIGMA, 12 (2016), 028, 34 pp.  mathnet  crossref
    2. Chicherin D., Derkachov S.E., Spiridonov V.P., “New Elliptic Solutions of the Yang–Baxter Equation”, Commun. Math. Phys., 345:2 (2016), 507–543  crossref  mathscinet  zmath  isi  elib  scopus
    3. D. Chicherin, V. P. Spiridonov, “The hyperbolic modular double and the Yang-Baxter equation”, Representation Theory, Special Functions and Painleve Equations - RIMS 2015, Advanced Studies in Pure Mathematics, 76, eds. H. Konno, H. Sakai, J. Shiraishi, T. Suzuki, Y. Yamada, Math Soc Japan, 2018, 95–123  mathscinet  isi
    4. Kamil Yu. Magadov, Vyacheslav P. Spiridonov, “Matrix Bailey Lemma and the Star-Triangle Relation”, SIGMA, 14 (2018), 121, 13 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:275
    Full text:63
    References:43
    First page:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020