Some Hecke algebra products and corresponding random walks |
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Authors: | Rosena R X Du Richard P Stanley |
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Institution: | 1.Department of Mathematics,East China Normal University,Shanghai,China;2.Department of Mathematics,M.I.T.,Cambridge,USA |
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Abstract: | Let i=1+q+???+q i?1. For certain sequences (r 1,…,r l ) of positive integers, we show that in the Hecke algebra ? n (q) of the symmetric group \(\mathfrak{S}_{n}\), the product \((1+\boldsymbol{r}_{\boldsymbol{1}}T_{r_{1}})\cdots (1+\boldsymbol{r}_{\boldsymbol{l}}T_{r_{l}})\) has a simple explicit expansion in terms of the standard basis {T w }. An interpretation is given in terms of random walks on \(\mathfrak{S}_{n}\). |
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