Geodesic
Some Hecke algebra products and corresponding random walks.
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 159-168.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\mathfrak S _{ n}$ mathfrakS_n , the product (1+ r $_{ 1} T _{ r $_1) frac14 (1+ r $_{ l} T _{ r $_ l) (1+boldsymbolr_boldsymbol1T_r_1)$\cdots $(1+boldsymbolr_boldsymbollT_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 $\mathfrak S _{ n}$ mathfrakS_n .
Keywords: keywords Hecke algebra, tight sequence, reduced decomposition, random walk 
@article{JAC_2010__31_1_a0,
     author = {Du, Rosena R.X. and Stanley, Richard P.},
     title = {Some {Hecke} algebra products and corresponding random walks.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {159--168},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a0/}
}
TY  - JOUR
AU  - Du, Rosena R.X.
AU  - Stanley, Richard P.
TI  - Some Hecke algebra products and corresponding random walks.
JO  - Journal of Algebraic Combinatorics
PY  - 2010
SP  - 159
EP  - 168
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a0/
LA  - en
ID  - JAC_2010__31_1_a0
ER  - 
%0 Journal Article
%A Du, Rosena R.X.
%A Stanley, Richard P.
%T Some Hecke algebra products and corresponding random walks.
%J Journal of Algebraic Combinatorics
%D 2010
%P 159-168
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a0/
%G en
%F JAC_2010__31_1_a0
Du, Rosena R.X.; Stanley, Richard P. Some Hecke algebra products and corresponding random walks.. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 159-168. http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a0/