theory of 
We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.


Recently, there is a renewed interest in wonderful varieties of rank two since they were shown to hold a keystone position in the theory of spherical varieties, see [L], [BP], and [K].


We relate the invariant theory of cones of highest weight vectors to weight multiplicities and theirqanalogs.


This paper shows how the KazhdanLusztig theory of cells can be directly applied to establish the quasiheredity ofqSchur algebras.


Using the path model and the theory of crystals, we generalize the concept of patterns to arbitrary complex semisimple algebraic groups.


We then give a combinatorial classification of reductive monoids by means of the theory of spherical varieties.


Using the theory of crystal bases as the main tool, we prove a quantum analogue of Richardson's theorem.


We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local structure and the intersection theory of aGvariety.


Then we apply the theory of KodairaSpencer for deformations of complex structures.


Geometric representation theory of restricted Lie algebras


We develop a theory of module categories over monoidal categories (this is a


In this paper we will describe the conjugacy classes and the invariant theory of this action.


KazhdanLusztig polynomials Px,w(q) play an important role in the study of Schubert varieties as well as the representation theory of semisimple Lie algebras.


Our basic tool is the representation theory of the Burkhardt group G = G25 920, which acts on our varieties.


In nonmodular invariant theory of finite groups, the


We develop a theory of perverse sheaves on the semiinfinite flag


The theory of PBW properties of quadratic algebras, to which this


In addition to the standard cohomological tools in algebraic geometry, the proof crucially relies on the nonvanishing of certain 3jsymbols from the quantum theory of


Explicit bounds on the number of type V variables in a complete system of typical separating invariants are given for the binary polyhedral groups, and this is applied to the invariant theory of binary


A Fock space approach to representation theory of osp(22n)

