Geodesic
A Hecke algebra quotient and some combinatorial applications
Journal of Algebraic Combinatorics, Tome 5 (1996) no. 3, pp. 175-189.

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

Summary: Let $( W, S)$ be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let $H$ be the corresponding Hecke Algebra. We define a certain quotient _boxclose_boxclose $\bar H$ of $H$ and show that it has a basis parametrized by a certain subset $W _{c}$ of the Coxeter group $W$. Specifically, $W _{c}$ consists of those elements of $W$ all of whose reduced expressions avoid substrings of the form $sts$ where $s$ and $t$ are noncommuting generators in $S$. We determine which Coxeter groups have finite $W _{c}$ and compute the cardinality of $W _{c}$ when $W$ is a Weyl group. Finally, we give a combinatorial application (which is related to the number of reduced expressions for [ `$( H)] \bar H$ .
Keywords: permutation, representation theory, non-commutative algebra, Lie theory, reductive group 
@article{JAC_1996__5_3_a3,
     author = {Fan, C.K.},
     title = {A {Hecke} algebra quotient and some combinatorial applications},
     journal = {Journal of Algebraic Combinatorics},
     pages = {175--189},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1996__5_3_a3/}
}
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Fan, C.K. A Hecke algebra quotient and some combinatorial applications. Journal of Algebraic Combinatorics, Tome 5 (1996) no. 3, pp. 175-189. http://geodesic.mathdoc.fr/item/JAC_1996__5_3_a3/