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the theory of finite group representations. Other topics ... affine cases, quantum groups, perverse sheaves, and rings of differential operators. Much of the ... sidered linear algebraic groups over an algebraically closed ground field of arbitrary ... It is shown moreover, by example, that for G of type B2, some higher cohomology. It is very well known that braids were rigorously defined by E. Artin ... the generalized braid groups of types C and D in terms of classical ones. ... canonical representation of the braid group Brn in the orthogonal group On induces a ... space and Hj ∈ V, j ∈ I be the finite family of complex affine hyperplanes given by linear.
In the following parts, among other things, we compute the Schwartz genus of the covering associated to the orbit space for all affine Artin groups. We also give a partial computation of the cohomology of the braid group with non-abelian coefficients coming from geometric representations.  Filippo Callegaro, Davide Moroni, and Mario Salvetti. Cohomology of affine Artin groups and applications. Trans. Amer. Math. Soc., 360(8):4169–4188, 2008.  Filippo Callegaro. Cohomology of finite and affine type Artin groups over abelian representations, volume 13 of Tesi. Scuola Normale Superiore di Pisa (Nuova Serie) [Theses of
Let G be a connected reductive group defined over an algebraically closed field k of characteristic p>0.The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the “order formula” of Testerman for unipotent elements in G; moreover, we show that the same formula determines the p-nilpotence degree of the corresponding nilpotent elements in the Lie algebra 22 Feb 2008 ... the Artin groups G˜An of affine type ˜An. By using a natural ... of Brn+1 found by Tong, Yang and Ma , twisted by an abelian representation. We also describe the cohomology of the braid group over the irreducible representation ... A Coxeter graph is a finite undirected graph, whose edges are labelled ...
can also be interpreted (and are so in Chapter 1.5) as cohomology groups of certain ... A group scheme G (say over a field) is called finite if the algebra of regular ... [Hoi] G. Hochschild: Introduction to Affine Algebraic Groups, San Francisco etc. ... Restricted representations of classical Lie algebras of types A2 and B2, Bull.
Serre gave a method using Galois cohomology and descent to classify reductive groups over an arbitrary field . For tori, a theorem of Grothendieck ensures that if two tori and over become isomorphic over , then they are actually isomorphic over a finite separable extension of (i.e., the scheme of tori is smooth). Below is a list of PhD dissertations written by students at the Harvard Department of Mathematics. All scholars can order copies of most Harvard dissertations from 1982 to the present by contacting UMI/ProQuest at 1-800-521-3042.