Let (W,S) be an irreducible Weyl or affine Weyl group. In [18], we constructed an algorithm for finding a representative set of left cells (or an l.c.r. set for short) of W in a two-sided cell Ω. In the present paper, we introduce a new simpler algorithm for finding an l.c.r. set of W in Ω when the subset F (Ω) of Ω is known (see Algorithm 3.11). Some technical tricks are introduced by some exa...

Let W be a finite or an affine Coxeter group and Wc the set of all the fully commutative elements in W . For any left cell L of W containing some fully commutative element, our main result of the paper is to prove that there exists a unique element (say wL) in L ∩ Wc such that any z ∈ L has the form z = xwL with `(z) = `(x) + `(wL) for some x ∈ W . This implies that L is left connected, verifyi...

This thesis is concerned with the intrinsic structure of the De Concini-Procesi compactification of semi-simple adjoint algebraic groups and some relations with other topics of algebraic groups. In chapter 1, we study the closure of the totally positive part of an adjoint group in the group compactification. One result that we obtain is the positive property of the closure with respect to the c...

Let G $G$ be a reductive algebraic group over an algebraically closed field k $\mathbb {k}$ of pretty good characteristic. The Lusztig–Vogan bijection is between the set dominant weights for and irreducible -equivariant vector bundles on nilpotent orbits, conjectured by Lusztig Vogan independently, constructed in full generality Bezrukavnikov. In characteristic 0, this related to theory 2-sided...

Program Monday 08h30-09h30 G. Lusztig: On the cleanness of cuspidal character sheaves. 09h45-10h45 P. Achar: Derived Satake equivalence and geometric restriction to a Levi subgroup. 11h15-12h15 G. Williamson: Generators and relations for Soergel bimodules. Tuesday 08h30-09h30 O. Brunat: On semisimple classes in finite reductive groups. 09h45-10h45 R. Charney: Groups Associated to Random Graphs....

Let %‘A be the category of finite dimensional right modules for a quasi-hereditary algebra A. In the context of various types of Kazhdan-Lusztig theories, we study both the homological dual A! = Extt, (A/ rad(A), A/ rad(A)) and the graded algebra grA = @rad(A)j/rad(A)j+‘. For example, we investigate a condition introduced in [6], and here called (SKL’), which guarantees that A!’ E gr A. A stren...