Involutions in Weyl Groups

نویسنده

  • ROBERT E. KOTTWITZ
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Calculating Canonical Distinguished Involutions in the Affine Weyl Groups

Distinguished involutions in the affine Weyl groups, defined by G. Lusztig, play an essential role in the Kazhdan-Lusztig combinatorics of these groups. A distinguished involution is called canonical if it is the shortest element in its double coset with respect to the finite Weyl group. Each two-sided cell in the affine Weyl group contains precisely one canonical distinguished involution. In t...

متن کامل

Models and refined models for involutory reflection groups and classical Weyl groups

A finite subgroup G of GL(n,C) is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group, i.e. elements g ∈ G such that gḡ = 1, where the bar denotes complex conjugation. A uniform combinatorial model is constructed for all non-exceptional irreducible complex reflection groups which are involutory including,...

متن کامل

The Weyl Group as Xed Point Set of Smooth Involutions

We show that the Weyl group W = M 0 =M of a noncompact semisimple Lie group is obtained by taking xed point sets of smooth involutions in K=M. More precisely, one considers rst the xed point set X of the involutions deened on K=M by the elements of order 2 in exp ia. The Weyl group is either X , or the xed point set of the involutions deened on X by special elements of order 4 in exp ia.

متن کامل

Fully 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 کامل

Commuting Involution Graphs for Ãn

Let G be a group and X a subset of G. The commuting graph on X, denoted C(G,X), has vertex set X and an edge joining x, y ∈ X whenever xy = yx. If in addition X is a set of involutions, then C(G,X) is called a commuting involution graph. Commuting graphs have been investigated by many authors. Sometimes they are tools used in the proof of a theorem, or they may be studied as a way of shedding l...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000