Monoid Hecke algebras

Putcha, Mohan

doi:10.1090/S0002-9947-97-01823-0

Monoid Hecke algebras
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by Mohan S. Putcha PDF

Trans. Amer. Math. Soc. 349 (1997), 3517-3534 Request permission

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 $R$,
extend the Kazhdan-Lusztig involution and basis to $\mathcal {H}$, and
prove, for a $W\times W$ orbit of $R$, the existence (conjectured by Renner) of generalized Kazhdan-Lusztig polynomials.

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