Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




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

Symmetry, Integrability and Geometry: Methods and Applications, 2005, Volume 1, 016, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2005.016 (Mi sigma16) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials

Valentyna Groza

National Aviation University, 1 Komarov Ave., Kyiv, 03058 Ukraine
Full-text PDF (171 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2005.016
Abstract: We derive orthogonality relations for discrete $q$-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra $\mathrm{su}_q(1,1)$. Spectra and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthonormal basis in the representation space.
Keywords: Quantum algebra $su_q(1,1)$; representations; discrete $q$-ultraspherical polynomials.
Received: September 16, 2005; in final form November 9, 2005; Published online November 15, 2005
Bibliographic databases:
Document Type: Article
MSC: 17B37; 33D45
Language: English
Citation: Valentyna Groza, “Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials”, SIGMA, 1 (2005), 016, 7 pp.
Citation in format AMSBIB
\Bibitem{Gro05}
\by Valentyna Groza
\paper Representations of the Quantum Algebra $\mathrm{su}_q(1,1)$ and Discrete $q$-Ultraspherical Polynomials
\jour SIGMA
\yr 2005
\vol 1
\papernumber 016
\totalpages 7
\mathnet{http://mi.mathnet.ru/sigma16}
\crossref{https://doi.org/10.3842/SIGMA.2005.016}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2169839}
\zmath{https://zbmath.org/?q=an:1128.17013}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000207064600016}
Linking options:
  • https://www.mathnet.ru/eng/sigma16
  • https://www.mathnet.ru/eng/sigma/v1/p16
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:147
    Full-text PDF :45
    References:34
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024