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Koszul Duality Patterns in Representation Theory
The aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of Koszul duality to repre- sentation theory. The paper consists of three parts
Representations of quantum groups at a p-th root of unity and of semisimple groups in characteristic p : independence of p
The method disclosed herein may be practiced by passing the vapors to be sampled along a path with halogen vapor, preferably chlorine vapor, heating the mixed vapors to halogenate those of the
Character formulas for tilting modules over Kac-Moody algebras
We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles, in
Kazhdan-Lusztig polynomials and a combinatoric for tilting modules
This article gives a self-contained treatment of the theory of Kazhdan-Lusztig polynomials with special emphasis on affine reflection groups. There are only a few new results but several new proofs.
The composition series of modules induced from Whittaker modules
AbstractWe study a category of representations over a semisimple Lie algebra, which contains category $ \cal O $ as well as the so-called Whittaker modules, and prove a generalization of the
n-Cohomology of simple highest weight modules on walls and purity
SummaryLetG⊃P⊃B be respectively a complex connected linear algebraic semisimple group, a parabolic subgroup and a Borel subgroup. The first main result is the following theorem: Let ℱ be a pure