Glasnik Matematicki, Vol. 57, No. 1 (2022), 17-33. \( \)

FINITE W-ALGEBRAS ASSOCIATED TO TRUNCATED CURRENT LIE ALGEBRAS

Xiao He

Paris Curie Engineer School, Beijing University of Chemical Technology, P.R.China
e-mail:hexiao@amss.ac.cn

Abstract.   Finite W-algebras associated to truncated current Lie algebras are studied in this paper. We show that some properties of finite W-algebras in the semisimple case hold in the truncated current case. In particular, Kostant's theorem and Skryabin equivalence hold in our case. As an application, we give a classification of simple Whittaker modules for truncated current Lie algebras in the \(s\ell_2\) case.

2020 Mathematics Subject Classification.   17B56, 17B70, 17B81

Key words and phrases.   Truncated current Lie algebras, Finite W-algebras, Skryabin equivalence, Whittaker modules.

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https://doi.org/10.3336/gm.57.1.02

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