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A q-analogue of an identity of N. Wallach

G. Lusztig
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Abstract

N.Wallach has considered an element of the group algebra of the symmetric group S_n which is the sum of an n-cycle, an (n-1)-cycle,...,a 2-cycle and the identity. He showed that multiplication by this element has eigenvalues 0,1,2,...,n-2,n. We prove a q-analogue of this result in which the group algebra of S_n is replaced by the corresponding Hecke algebra.

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G. Lusztig. 2003-11-11. A q-analogue of an identity of N. Wallach. https://arxiv.org/abs/math/0311158

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