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Monoid Hecke algebras


Author: Mohan S. Putcha
Journal: Trans. Amer. Math. Soc. 349 (1997), 3517-3534
MSC (1991): Primary 20G40, 20G05, 20M30
DOI: https://doi.org/10.1090/S0002-9947-97-01823-0
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:

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


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Additional Information

Mohan S. Putcha
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
Email: putcha@math.ncsu.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01823-0
Received by editor(s): December 3, 1993
Additional Notes: Research partially supported by NSF Grant DMS9200077
Article copyright: © Copyright 1997 American Mathematical Society

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