Vol. 273, No. 1, 2015

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On Whittaker modules for a Lie algebra arising from the 2-dimensional torus

Shaobin Tan, Qing Wang and Chengkang Xu

Vol. 273 (2015), No. 1, 147–167
Abstract

Let A be the ring of Laurent polynomials in two variables and B be the set of skew derivations of A. We denote by L̃ the semidirect product of A and B, and by L the universal central extension of the derived Lie algebra of L̃. We study the Whittaker modules for the Lie algebra L. The irreducibilities for the universal Whittaker modules are given. Moreover, a -gradation is defined on the universal Whittaker modules and we determine all -graded irreducible quotients of the reducible universal Whittaker modules.

Keywords
Whittaker module, infinite-dimensional Lie algebra, torus
Mathematical Subject Classification 2010
Primary: 06B15
Secondary: 17B65, 17B66
Milestones
Received: 7 December 2013
Accepted: 6 May 2014
Published: 6 December 2014
Authors
Shaobin Tan
School of Mathematical Sciences
Xiamen University
Xiamen 361005
China
Qing Wang
School of Mathematical Sciences
Xiamen University
Xiamen 361005
China
Chengkang Xu
School of Mathematical Sciences
Xiamen University
Xiamen 361005
China