منابع مشابه
The affine Hecke algebra
1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...
متن کاملCyclage, Catabolism, and the Affine Hecke Algebra
We identify a subalgebra Ĥ + n of the extended affine Hecke algebra Ĥn of type A. The subalgebra Ĥ + n is a u-analogue of the monoid algebra of Sn⋉Z n ≥0 and inherits a canonical basis from that of Ĥn. We show that its left cells are naturally labeled by tableaux filled with positive integer entries having distinct residues mod n, which we term positive affine tableaux (PAT). We then exhibit a ...
متن کاملMultiplicity matrices for the affine graded Hecke algebra
In this paper we are looking 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 [9, 10], and use them in particular to compute, at every real central character which admits tempered modules, the geometric parameterization, the Kazhdan-Lusztig polynomials, the composition s...
متن کاملFinite - difference representations of the degenerate affine Hecke algebra
The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The sl(m)-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebr...
متن کاملThe Spherical Hecke Algebra for Affine Kac-moody Groups I
We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomorphism for these algebras, relating it to integrable representations of the Langlands dual affine Kac-Moody group. In the next publication we shall use these results to define and study the notion of Hecke eigenfunction for the group Ga...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2014
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748014000188