A geometric interpretation for characters of Iwahori--Hecke algebras

Abstract: The Iwahori-Hecke algebra is a deformation of the group algebra of the symmetric group. It has a distinguished basis (enumerated by permutations) called the Kazhdan-Lusztig basis. For each permutation we consider certain subvarieties of the complete flag variety that generalize Hessenberg varieties. These varieties carry an action of the symmetric group on its intersection cohomology groups. We prove that the Frobenius character of this action is precisely the Frobenius character of an element of the Kazhdan-Lusztig basis of the Hecke algebra. This is a generalization to non-codominant permutations of Brosnan-Chow's solution to the Sharesian-Wachs conjecture. Some partial results in other Lie types are also achieved.

algebraic geometry

Audience: researchers in the topic

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Brazilian algebraic geometry seminar

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