Whittaker modules for the insertion-elimination Lie algebra
Representation Theory
2015-10-26 v1
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 a Whittaker module corresponding to a given algebra homomorphism. Among other results, we show that the standard Whittaker module is simple given certain constraints on the corresponding algebra homomorphism.
Cite
@article{arxiv.1510.06998,
title = {Whittaker modules for the insertion-elimination Lie algebra},
author = {Matthew Ondrus and Emilie Wiesner},
journal= {arXiv preprint arXiv:1510.06998},
year = {2015}
}