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Invariant Algebra and Cuspidal Representations of Finite Monoids

✍ Scribed by Mohan S Putcha

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
120 KB
Volume
212
Category
Article
ISSN
0021-8693

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✦ Synopsis

Motivated by the theories of Hecke algebras and Schur algebras, we consider in this paper the algebra ‫ރ‬ M G of G-invariants of a finite monoid M with unit group G. If M is a regular ''balanced'' monoid, we show that ‫ރ‬ M G is a quasi-hereditary algebra. In such a case, we find the blocks of ‫ރ‬ M G to be the ''sections'' of the blocks of ‫ރ‬ M. We go on to develop a theory of cuspidal representations for balanced monoids. We then apply our results to the full transformation semigroup and the multiplicative monoid of triangular matrices over a finite field. ᮊ 1999

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