Monoid Hecke algebras
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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 twosided 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 KazhdanLusztig involution and basis to $\mathcal {H}$, and

prove, for a $W\times W$ orbit of $R$, the existence (conjectured by Renner) of generalized KazhdanLusztig polynomials.
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Additional Information
 Mohan S. Putcha
 Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 276958205
 Email: putcha@math.ncsu.edu
 Received by editor(s): December 3, 1993
 Additional Notes: Research partially supported by NSF Grant DMS9200077
 © Copyright 1997 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 349 (1997), 35173534
 MSC (1991): Primary 20G40, 20G05, 20M30
 DOI: https://doi.org/10.1090/S0002994797018230
 MathSciNet review: 1401527