Basis of Hecke algebras - associated to Coxeter groups - via matrices of inversion for permutations

Abstract

Applying the matrices of inversion for permutations, we show that every element of S_{n} associates a unique canonical word in the Hecke algebra H_{n-1}(z). That provides an effective and simple algorithm for counting a linear basis of Hecke algebra H_{n}, as binary matrices.