Hecke Algebra Actions on the Coinvariant Algebra
Ron M. Adin, Alexander Postnikov, Yuval Roichman
Abstract
Two actions of the Hecke algebra of type A on the corresponding polynomial ring are studied. Both are deformations of the natural action of the symmetric group on polynomials, and keep symmetric functions invariant. We give an explicit description of these actions, and deduce a combinatorial formula for the resulting graded characters on the coinvariant algebra.
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