Fundamental elements of an affine Weyl group
نویسندگان
چکیده
منابع مشابه
Partial orderings of an affine Weyl group
In this note we draw together some of the scattered literature dealing with several partial orderings of affine Weyl groups. Most of the theory was developed as a tool in the study of modular representations for groups of Lie type, but here we focus just on an affine Weyl group Wa in its elementary geometric setting while sometimes invoking also its structure as a Coxeter group. While notation ...
متن کاملFully Commutative Elements in the Weyl and Affine Weyl Groups
Let W be a Weyl or affine Weyl group and let Wc be the set of fully commutative elements in W . We associate each w ∈ Wc to a digraph G(w). By using G(w), we give a graph-theoretic description for Lusztig’s a-function on Wc and describe explicitly all the distinguished involutions of W . The results verify two conjectures in our case: one was proposed by myself in [15, Conjecture 8.10] and the ...
متن کاملAffine Weyl Group Approach to Painlevé Equations
An overview is given on recent developments in the affine Weyl group approach to Painlevé equations and discrete Painlevé equations, based on the joint work with Y. Yamada and K. Kajiwara. 2000 Mathematics Subject Classification: 34M55, 39A12, 37K35.
متن کاملOn Dominance and Minuscule Weyl Group Elements
Fix a Dynkin graph and let λ be a coweight. When does there exist an element w of the corresponding Weyl group such that w is λ-minuscule and w(λ) is dominant? We answer this question for general Coxeter groups. We express and prove these results using a variant of Mozes’s game of numbers.
متن کاملElliptic Weyl Group Elements and Unipotent Isometries
Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...
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: Mathematische Annalen
سال: 2014
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-014-1122-7