Some Hecke Algebra Products and Corresponding Random Walks

2008/09/01 by Rosena R. X. Du, Richard P. Stanley, Du, Rosena R. X. +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #05E99 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Fractal and DNA sequence analysis #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0809.0166

openalex publication_date 2008/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \bmi=1+q+...+q^i-1. For certain sequences (r₁,...,r_l) of positive integers, we show that in the Hecke algebra \mathscrH_n(q) of the symmetric group \mathfrakS_n, the product (1+\bmr₁T_r1)... (1+\bmr_lT_rl) has a simple explicit expansion in terms of the standard basis \T_w\. An interpretation is given in terms of random walks on \mathfrakS_n.

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