In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre sented a 30-
hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and …

Nilpotent Orbits in Representation Theory Page 1 Nilpotent Orbits in Representation Theory
Jens Carsten Jantzen Department of Mathematics Ny Munkegade, DK-8000 Aarhus C, Denmark …

Let G be a simple, simply connected algebraic group over C, g= Lie G, N (g) the nilpotent
cone of g, and (E, H, F) an sl 2-triple in g. Let S= E+ Ker ad F, the special transverse slice to …

We show that, on the level of derived categories, representations of the Lie algebra of a
semisimple algebraic group over a field of finite characteristic with a given (generalized) …

We introduce a new class of algebras called Poisson orders. This class includes the
symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of …

We prove most of Lusztig's conjectures on the canonical basis in homology of a Springer
fiber. The conjectures predict that this basis controls numerics of representations of the Lie …

This paper introduces baby Verma modules for symplectic reflection algebras of complex
reflection groups at parameter t= 0 (the so‐called rational Cherednik algebras at parameter …

R.–Dans cet article nous construisons et étudions une action du groupe de tresses affine
associé à un groupe algébrique semi-simple sur les catégories dérivées de faisceaux …

Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a
central role in geometric representation theory. A new structure on this variety has arisen in …

We compute the Azumaya loci of Kauffman-bracket skein algebras of closed surfaces at odd
roots of unity and provide partial results for open surfaces as well. As applications, we give …