Monoid Hecke algebras
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- by Mohan S. Putcha PDF
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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:
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find a description of the irreducible representations of $\mathcal {H}$,
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find an explicit isomorphism between $\mathcal {H}$ and the monoid algebra of the Renner monoid $R$,
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extend the Kazhdan-Lusztig involution and basis to $\mathcal {H}$, and
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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
- 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), 3517-3534
- MSC (1991): Primary 20G40, 20G05, 20M30
- DOI: https://doi.org/10.1090/S0002-9947-97-01823-0
- MathSciNet review: 1401527