Lifting involutions in a Weyl group to the torus normalizer
نویسندگان
چکیده
منابع مشابه
Involutions in Weyl Groups
Let G be a split real group with Weyl group W . Let E be an irreducible representation of W . Let V be the stable Lie algebra version of the coherent continuation representation of W . The main result of this paper is a formula for the multiplicity of E in V . The formula involves the position of E in Lusztig’s set ∐ M(G). The paper treats all quasi-split groups G as well.
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Let (W,Σ) be a finite Coxeter system, and θ an involution such that θ(∆) = ∆, where ∆ is a basis for the root system Φ associated with W , and Iθ = {w ∈ W | θ(w) = w−1} the set of θ-twisted involutions in W . The elements of Iθ can be characterized by sequences in Σ which induce an ordering called the Bruhat poset. The main algorithm of this paper computes this poset. Algorithms for finding con...
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(Py,w;i ∈ N, u is an indeterminate) were defined and computed in terms of an algorithm for any y ≤ w in W . These polynomials are of interest for the representation theory of complex reductive groups, see [6]. Let I = {w ∈ W ;w2 = 1} be the set of involutions in W . In this paper we introduce some new polynomials P σ y,w = ∑ i≥0 P σ y,w;iu i (P σ y,w;i ∈ Z) for any pair y ≤ w of elements of I. ...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2018
ISSN: 1088-4165
DOI: 10.1090/ert/513