A character approach to Looijenga's invariant theory for generalized root systems
A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups
Let G be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous G-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence between Poisson homogeneous G-spaces and Lagrangian subalgebras in the double D𝖌 (here 𝖌 = Lie G). A geometric interpretation of some Poisson homogeneous G-spaces is also proposed.
A Clifford algebra approach to simple Lie algebras of real rank two. I: The case.
A generalization of the Enright-Varadarajan modules
A Geometric Realization of
A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras.
A Multiplicity One Theorem for Holomorphically Induced Representations.
A periodisation of semisimple Lie algebras.
A real analog of Kostant's version of the Bott-Borel-Weil theorem.
A refinement of the PRV conjecture.
A saturation property for powers of irreducible characters.
A trace formula for semi-simple Lie algebras
A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux.
Abelian ideals of a Borel subalgebra and root systems
Let be a simple Lie algebra and the poset of non-trivial abelian ideals of a fixed Borel subalgebra of . In [8], we constructed a partition parameterised by the long positive roots of and studied the subposets . In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of is a join-semilattice.
Abelian Varieties, l-adic Representations and Lie Algebras.
Adjoint vector fields on the tangent space of semisimple symmetric spaces.
Affine braid group actions on derived categories of Springer resolutions
In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...
Affine Root Systems and Dedekind's ?-Function.
Algorithmic orbit classification for some Borel group actions
An Algebraic Construction of a Class of Representations of a Semi-Simple Lie Algebra.