Hasegawa, Koji
Published in
Letters in Mathematical Physics

A discretization of Painlevé VI equation was obtained by Jimbo and Sakai (Lett Math Phys 38:145–154, 1996). There are two ways to quantize it: (1) use the affine Weyl group symmetry (of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepac...

Teff, Nicholas

We construct a divided difference operator using GKM theory. This generalizes the classical divided difference operator for the cohomology of the complete flag variety. This construction proves a special case of a recent conjecture of Shareshian and Wachs. Our methods are entirely combinatorial and algebraic, and rely heavily on the combinatorics o...

Fleig, Philipp Koehn, Michael Nicolai, Hermann
Published in
Letters in Mathematical Physics

We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac–Moody algebras. These domains are given as subsets of certain generalized upper half planes, on which the Weyl groups act via generalized modular transformations. Our construction only requires the Carta...

Schlage-Puchta, Jan-Christoph
Published in
Archiv der Mathematik

Let G be a finite group, A a finite abelian group. Each homomorphism \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi:G\rightarrow A\wr S_n}$$\end{document} ind...

Burdges, Jeffrey Deloro, Adrien
Published in
Israel Journal of Mathematics

We examine Weyl groups of minimal connected simple groups of finite Morley rank of degenerate type. We show that they are cyclic, and lift isomorphically to subgroups of the ambient group.

Azam, Saeid Shahsanaei, Valiollah
Published in
Journal of Algebraic Combinatorics

It is known that elliptic Weyl groups, extended affine Weyl groups of nullity 2, have a finite presentation called the generalized Coexter presentation. Similar to the finite and affine case this presentation is obtained by assigning a Dynkin diagram to the root system. Then there is a prescription to read the generators and relations from the diag...

Juteau, Daniel

In 1976, Springer defined a correspondence making a link between the irreducible ordinary (characteristic zero) representations of a Weyl group and the geometry of the associated nilpotent variety. In this thesis, we define a modular Springer correspondence (in positive characteristic), and we show that the decomposition numbers of a Weyl group (fo...

Bonnafé, Cédric

The aim of this second part is to compute explicitly the Lusztig restriction of the characteristic function of a regular unipotent class of a finite reductive group, improving slightly a theorem of Digne, Lehrer and Michel. We follow their proof but introduce new information, namely the computation of morphisms $\varphi_{L,v}^G$ defined in the firs...

Hezard, David

Soit G un groupe algébrique réductif connexe de centre connexe défini sur un corps fini de caractéristique p>0. On munit cette structure d'un endomorphisme de Frobenius F et l'on note G^F l'ensemble des points de G fixes pour l'action de F : G^F est un groupe fini. On suppose que la caractéristique p est bonne pour G.

On définit alors une applicatio...

Bonnafé, Cédric

We construct a new isomorphism between the endomorphism algebra of an induced cuspidal character sheaf and the group algebra of the relative Weyl group involved. We show it differs from Lusztig one by a linear character, and we relate this linear character to some stabilizers. Some consequences on characteristic functions of character sheaves are o...