Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
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

Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 199, Number 1, Pages 3–32
DOI: https://doi.org/10.4213/tmf9536 (Mi tmf9536) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Singular vectors of the Ding–Iohara–Miki algebra

Y. Ohkubo

Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, Japan
Full-text PDF (728 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf9536
Abstract: We review properties of generalized Macdonald functions arising from the AGT correspondence. In particular, we explain a coincidence between generalized Macdonald functions and singular vectors of a certain algebra $\mathcal{A}(N)$ obtained using the level-$(N,0)$ representation (horizontal representation) of the Ding–Iohara–Miki algebra. Moreover, we give a factored formula for the Kac determinant of $\mathcal{A}(N)$, which proves the conjecture that the Poincaré–Birkhoff–Witt-type vectors of the algebra $\mathcal{A}(N)$ form a basis in its representation space.
Keywords: AGT correspondence, Macdonald symmetric function, Ding–Iohara–Miki algebra, singular vector.
Funding agency Grant number
Japan Society for the Promotion of Science 18J00754
Canon Foundation Research Fellowship
This research was supported in part by a Canon Foundation Research Fellowship in 2017 and a Grant-in-Aid for a JSPS Research Fellow (Grant No. 18J00754) in 2018.
Received: 12.01.2018
Revised: 30.09.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 199, Issue 1, Pages 475–500
DOI: https://doi.org/10.1134/S0040577919040019
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Y. Ohkubo, “Singular vectors of the Ding–Iohara–Miki algebra”, TMF, 199:1 (2019), 3–32; Theoret. and Math. Phys., 199:1 (2019), 475–500
Citation in format AMSBIB
\Bibitem{Ohk19}
\by Y.~Ohkubo
\paper Singular vectors of the~Ding--Iohara--Miki algebra
\jour TMF
\yr 2019
\vol 199
\issue 1
\pages 3--32
\mathnet{http://mi.mathnet.ru/tmf9536}
\crossref{https://doi.org/10.4213/tmf9536}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3942838}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2019TMP...199..475O}
\elib{https://elibrary.ru/item.asp?id=37180608}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 199
\issue 1
\pages 475--500
\crossref{https://doi.org/10.1134/S0040577919040019}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000468116000001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85065734544}
Linking options:
  • https://www.mathnet.ru/eng/tmf9536
  • https://doi.org/10.4213/tmf9536
  • https://www.mathnet.ru/eng/tmf/v199/i1/p3
    • 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
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:278
    Full-text PDF :52
    References:27
    First page:11
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024