Title

Whittaker Modules for the Insertion-Elimination Lie Algebra

Document Type

Article

Publication Date

8-1-2017

Abstract

This paper addresses the representation theory of the insertion-elimination Lie algebra, a Lie algebra that can be naturally realized in terms of tree-inserting and tree-eliminating operations on rooted trees. The insertion-elimination algebra admits a triangular decomposition in the sense of Moody and Pianzola, and thus it is natural to define Whittaker modules corresponding to a given algebra homomorphism. Among other results, we show that the standard Whittaker modules are simple under certain constraints on the corresponding algebra homomorphism.

Publication Name

Algebras and Representation Theory

Volume Number

20

First Page

843

Last Page

856

Issue Number

4

DOI

10.1007/s10468-016-9665-9

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