相关论文: Admissible subsets and Littelmann paths in affine …

In this paper we consider the Hecke algebra $\mathcal {H}$ associated to an extended affine Weyl group of type $\widetilde{B_2}$. We give some interesting formulas on $C_{rt}S_{\lambda}$, which imply some relations between the…

The main result in this paper is the character formula for arbitrary irreducible highest weight modules of W algebras. The key ingredient is the functor provided by quantum Hamiltonian reduction, that constructs the W algebras from affine…

Lusztig proved that the Kazhdan-Lusztig basis of a spherical Hecke algebra can be essentially identified with the Weyl characters of the Langlands dual group. We generalize this result to the unequal parameter case. The new proof is pretty…

The Kazhdan-Lusztig parameters are important parameters in the representation theory of $p$-adic groups and affine Hecke algebras. We show that the Kazhdan-Lusztig parameters have a definite geometric structure, namely that of the extended…

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…

Let $\tilde{W}$ be an extended affine Weyl group, $\mathbf{H}$ be the corresponding affine Hecke algebra over the ring $\mathbb{C}[\mathbf{q}^\frac{1}{2}, \mathbf{q}^{-\frac{1}{2}}]$, and $J$ be Lusztig's asymptotic Hecke algebra, viewed as…

In this paper, we look at the problem of determining the composition factors for the affine graded Hecke algebra via the computation of Kazhdan-Lusztig type polynomials. We review the algorithms of \cite{L1,L2}, and use them in particular…

According to a conjecture of Lusztig, the asymptotic affine Hecke algebra should admit a description in terms of the Grothedieck group of sheaves on the square of a finite set equivariant under the action of the centralizer of a nilpotent…

To any element of a connected, simply connected, semisimple complex algebraic group G and a choice of an element of the corresponding Weyl group there is an associated Lusztig variety. When the element of G is regular semisimple, the…

We show that the Kazhdan-Lusztig basis elements $C_w$ of the Hecke algebra of the symmetric group, when $w \in S_n$ corresponds to a Schubert subvariety of a Grassmann variety, can be written as a product of factors of the form…

Let W be a Coxeter group and L be a weight function on W. Following Lusztig, we have a corresponding decomposition of W into left cells, which have important applications in representation theory. We study the case where $W$ is an affine…

For irreducible characters $\{ \chi_q^\lambda \,|\, \lambda \vdash n \}$, induced sign characters $\{ \epsilon_q^\lambda \,|\, \lambda \vdash n \}$, and induced trivial characters $\{ \eta_q^\lambda \,|\, \lambda \vdash n \}$ of the Hecke…

Let $R$ be a root datum with affine Weyl group $W^e$, and let $H = H (R,q)$ be an affine Hecke algebra with positive, possibly unequal, parameters $q$. Then $H$ is a deformation of the group algebra $\mathbb C [W^e]$, so it is natural to…

We construct a bijection between admissible representations for an affine Lie algebra $\mathfrak{g}$ at boundary admissible levels and $\mathbb{C}^\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual…

Take the degenerate affine Hecke algebra $H_{l+m}$ corresponding to the group $GL_{l+m}$ over a $p$-adic field. Consider the $H_{l+m}$-module $W$ induced from the tensor product of the evaluation modules over the algebras $H_l$ and $H_m$.…

By Tits' deformation argument, a generic Iwahori--Hecke algebra $H$ associated to a finite Coxeter group $W$ is abstractly isomorphic to the group algebra of $W$. Lusztig has shown how one can construct an explicit isomorphism, provided…

Admissible W-graphs were defined and combinatorially characterised by Stembridge in reference [12]. The theory of admissible W-graphs was motivated by the need to construct W-graphs for Kazhdan-Lusztig cells, which play an important role in…

We introduce a representation of the double affine Hecke algebra at the critical level q=1 in terms of difference-reflection operators and use it to construct an explicit integrable discrete Laplacian on the Weyl alcove corresponding to an…

Let G be a semisimple algebraic group over an algebraically closed field of characteristic p>0, and let g be its Lie algebra. The crucial Lie algebra representations to understand are those associated with the reduced enveloping algebra…

We prove a conjecture by Lusztig, which describes the tensor categories of perverse sheaves on affine flag manifolds, with tensor structure provided by truncated convolution, in terms of the Langlands dual group. We also give a geometric…