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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
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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
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    • This publication is cited in the following 1 articles:
    1. B. Le Floch, “A slow review of the AGT correspondence”, J. Phys. A: Math. Theor., 55:35 (2022), 353002  crossref
    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
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    References:39
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