A New Proof for Classification of Irreducible Modules of a Hecke Algebra of Type An A_n

In this paper we give a new proof for the classification of irreducible modules of an affine Hecke algebra of type $A_n$, which was obtained by G. E. Murphy in 1995.Comment: 9 page

Module Structure on Invariant Jacobians

In this paper we show that a conjecture of Stephen Yau on highest weights of invariant Jacobians is true for arbitrary connected semisimple algebraic groups.Comment: 3 page

The leading coefficient of certain Kazhdan-Lusztig polynomials of the permutation group SnS_n

In this paper we show that the leading coefficient $\mu(y,w)$ of certain Kazhdan-Lusztig polynomials $P_{y,w}$ of the permutation group $\mathfrak S_n$ of 1,2,...,n are not greater than 1. More precisely, we show that the leading coefficients $\mu(y,w)$ are not greater than 1 whenever $a(y)< a(w)$, where $a: \mathfrak S_n\to\mathbf N$ is the function defined by Lusztig.Comment: 7 page