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Representations of the Renner Monoid

Authors
  • Li, Zhuo
  • Li, Zhenheng
  • Cao, You'an
Type
Preprint
Publication Date
Dec 05, 2008
Submission Date
Dec 05, 2008
Identifiers
arXiv ID: 0812.1173
Source
arXiv
License
Yellow
External links

Abstract

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups determine the complete set of irreducible representations of the Renner monoids. An analogue of the Munn-Solomon formula for calculating the character of the Renner monoids, in terms of the characters of the parabolic subgroups, is shown.

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