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Whittaker Modules for the Insertion-Elimination Lie Algebra

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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.

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Authors and Affiliations

  1. Mathematics Department, Weber State University, Ogden, UT, 84408, USA

    Matthew Ondrus

  2. Department of Mathematics, Ithaca College, 953 Danby Rd, Ithaca, NY, 14850, USA

    Emilie Wiesner

Authors
  1. Matthew Ondrus
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  2. Emilie Wiesner
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Correspondence to Emilie Wiesner.

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Presented by Vyjayanthi Chari.

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Ondrus, M., Wiesner, E. Whittaker Modules for the Insertion-Elimination Lie Algebra. Algebr Represent Theor 20, 843–856 (2017). https://doi.org/10.1007/s10468-016-9665-9

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  • DOI: https://doi.org/10.1007/s10468-016-9665-9

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