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ISSN 1088-6850(e) ISSN 0002-9947(p)

Monoid Hecke algebras

Author(s): Mohan S. Putcha
Journal: Trans. Amer. Math. Soc. 349 (1997), 3517-3534.
MSC (1991): Primary 20G40, 20G05, 20M30
MathSciNet review: 1401527
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Abstract: This paper concerns the monoid Hecke algebras $\mathcal {H}$ introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group $W$ . We use this to:

find a description of the irreducible representations of $\mathcal {H}$ ,
find an explicit isomorphism between $\mathcal {H}$ and the monoid algebra of the Renner monoid ,
extend the Kazhdan-Lusztig involution and basis to $\mathcal {H}$ , and
prove, for a $W\times W$ orbit of , the existence (conjectured by Renner) of generalized Kazhdan-Lusztig polynomials.

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