Some Hecke algebra products and corresponding random walks
Rosena R.X. Du
and Richard P. Stanley
DOI: 10.1007/s10801-009-0193-0
Abstract
Let i=1+ q+ \cdot \cdot \cdot + q i - 1. For certain sequences ( r 1,\cdots , r l ) of positive integers, we show that in the Hecke algebra \Bbb H n ( q) of the symmetric group \mathfrak S n \mathfrak{S}_{n} , the product (1+ r 1 T r 1) \frac{1}{4} (1+ r l T r l) (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 \mathfrak{S}_{n} .
Pages: 159–168
Keywords: keywords Hecke algebra; tight sequence; reduced decomposition; random walk
Full Text: PDF
References
1. Cherednik, I.V.: Special bases of irreducible representations of a degenerate affine Hecke algebra.