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Sandwich matrices, Solomon algebras, and Kazhdan-Lusztig polynomials


Author: Mohan S. Putcha
Journal: Trans. Amer. Math. Soc. 340 (1993), 415-428
MSC: Primary 20M30; Secondary 20G05
DOI: https://doi.org/10.1090/S0002-9947-1993-1127157-2
MathSciNet review: 1127157
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Abstract: Sandwich matrices have proved to be of importance in semigroup theory for the last 50 years. The work of the author on algebraic monoids leads to sandwich matrices in group theory. In this paper, we find some connections between sandwich matrices and the Hecke algebras (for monoids) introduced recently by Louis Solomon. At the local level we then obtain an explicit isomorphism between Solomon's Hecke algebra and the complex monoid algebra of the Renner monoid. In the simplest case of monoids associated with a Borel subgroup, we find that the entries of the inverse of the sandwich matrix, as well as those of the related structure matrix of Solomon's Hecke algebra are 'almost' the polynomials $ {R_{x,y}}$ associated with the Kazhdan-Lusztig polynomials.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1127157-2
Article copyright: © Copyright 1993 American Mathematical Society

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