相关论文: Centres of Hecke algebras: the Dipper-James conjec…

We describe a recursive algorithm that produces an integral basis for the centre of the Hecke algebra of type A consisting of linear combinations of monomial symmetric polynomials of Jucys--Murphy elements. We also discuss the existence of…

G. E. Murphy showed in 1983 that the centre of every symmetric group algebra has an integral basis consisting of a specific set of monomial symmetric polynomials in the Jucys--Murphy elements. While we have shown in earlier work that the…

We give an algebraic description of the equivariant K-theory of Gieseker varieties. Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy center of the cyclotomic Hecke algebra, over the…

A celebrated result of Farahat and Higman constructs an algebra $\mathrm{FH}$ which "interpolates" the centres $Z(\mathbb{Z}S_n)$ of group algebras of the symmetric groups $S_n$. We extend these results from symmetric group algebras to type…

We provide a dual version of the Geck--Rouquier Theorem on the center of an Iwahori--Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank $2$, for which the symmetrising trace conjecture is…

In this paper we investigate non-central elements of the Iwahori-Hecke algebra of the symmetric group whose squares are central. In particular, we describe a commutative subalgebra generated by certain non-central square roots of central…

We introduce some modified forms for the degenerate and non-degenerate affine Hecke algebras of type $A$. These are certain subalgebras living inside the inverse limit of cyclotomic Hecke algebras. We construct faithful representations and…

Using norms, the second author constructed a basis for the centre of the Hecke algebra of the symmetric group over $\Q[\xi]$ in 1990. An integral "minimal" basis was later given by the first author in 1999, following work of Geck and…

In this paper we show that the center of the partition algebra $\mathcal{A}_{2k}(\delta)$, in the semisimple case, is given by the subalgebra of supersymmetric polynomials in the normalised Jucys-Murphy elements. For the non-semisimple…

We study symmetric polynomials whose variables are odd-numbered Jucys-Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric group with the hyperoctahedral group. We evaluate their…

Let R be an integral domain and A a cellular algebra. Suppose that A is equipped with a family of Jucys-Murphy elements which satisfy the separation condition. Let K be the field of fractions of R. We give a necessary and sufficient…

We study a commuting family of elements of the walled Brauer algebra $B_{r,s}(\delta)$, called the Jucys-Murphy elements, and show that the supersymmetric polynomials in these elements belong to the center of the walled Brauer algebra. When…

We give an explicit expression for the central elements of affine Hecke algebras of type A in the Coxeter presentation, in terms of (parabolic) affine Kazhdan-Lusztig polynomials. Our approach is based on a version of quantum affine…

This paper proves a periodic property of Jucys-Murphy elements of the degenerate and non-degenerate cy- clotomic Hecke algebras of type A. We do this by first giving a new closed formula for the KLR idempotents e(i) which, it tuns out, is…

An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy elements using representations of the simplest affine Hecke…

We show that the center of the Iwahori--Hecke algebra of the symmetric group $S_n$ carries a natural filtered algebra structure, and that the structure constants of the associated graded algebra are independent of $n$. A series of…

Let $\mathscr{H}_n$ denote the Iwahori-Hecke algebra corresponding to the symmetric group $\mathfrak{S}_n$. We set up a Green correspondence for bimodules of these Hecke algebras, and a Brauer correspondence between their blocks. We examine…

We use Bernstein's presentation of the Iwahori-Matsumoto Hecke algebra to obtain a simple proof of the Satake isomorphism and, in the same stroke, compute the center of the Iwahori-Matsumoto Hecke algebra.

We give half a dozen bases of the Hecke algebra of the symmetric group, and relate them to the basis of Geck-Rouquier, and to the basis of Jones, using matrices of change of bases of the ring of symmetric polynomials.

An approach, based on Jucys--Murphy elements, to the representation theory of cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra) of the set of the Jucys--Murphy elements is established. A basis of the…