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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Sandwich matrices, Solomon algebras, and Kazhdan-Lusztig polynomials
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by Mohan S. Putcha PDF
Trans. Amer. Math. Soc. 340 (1993), 415-428 Request permission

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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • 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