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Letters in Mathematical Physics

, Volume 109, Issue 1, pp 33–60 | Cite as

Kac determinant and singular vector of the level N representation of Ding–Iohara–Miki algebra

  • Yusuke OhkuboEmail author
Article

Abstract

In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level N representation of the Ding–Iohara–Miki algebra. It is also discovered that its singular vectors correspond to generalized Macdonald functions (the q-deformed version of the AFLT basis).

Keywords

Macdonald symmetric function Ding–Iohara–Miki algebra AGT correspondence 

Mathematics Subject Classification

81R10 33D52 81R50 

Notes

Acknowledgements

The author shows his greatest appreciation to H. Awata, M. Bershtein, B. Feigin, P. Gavrylenko, K. Hosomichi, H. Itoyama, H. Kanno, A. Marshakov, T. Matsumoto, A. Mironov, S. Moriyama, Al. Morozov, An. Morozov, H. Nagoya, A. Negut, T. Okazaki, T. Shiromizu, T. Takebe, M. Taki, S. Yanagida and Y. Zenkevich for variable discussions and comments. The author is supported in part by Canon Foundation Research Fellowship.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsThe National Research University Higher School of EconomicsMoscowRussian Federation

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