New Unitary Representations of Loop Groups.
Nilpotent Lie algebras of maximal rank and of Kac-Moody type .
On a diffeological group realization of certain generalized symmetrizable Kac-Moody Lie algebras.
On affine Kac-Moody Lie algebras
On brane solutions related to non-singular Kac-Moody algebras.
On deformations and contractions of Lie algebras.
On formal series and infinite products over Lie algebras.
On some modular representations of affine Kac-Moody algebras at the critical level
On the basic representation of the affine Kac-Moody Lie algebras
On the combinatorics of Kac's asymmetry function
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is...
On the nilpotency of certain subalgebras of Kac-Moody Lie algebras.
Poisson-Lie groups and complete integrability. I. Drinfeld bigebras, dual extensions and their canonical representations
Prescribed Gauss decompositions for Kac-Moody groups over fields
Product formulas for modular forms on
Projections of singular vectors of Verma modules over rank 2 Kac-Moody Lie algebras.
Quantization of Drinfeld Zastava in type
Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra . We introduce an affine, reduced, irreducible, normal quiver variety which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian...
Quantum groups in higher genus and Drinfeld’s new realizations method ( case)
Quasi-particle fermionic formulas for (k, 3)-admissible configurations
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.
Quiver varieties and the character ring of general linear groups over finite fields
Given a tuple of irreducible characters of we define a star-shaped quiver together with a dimension vector . Assume that is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied, we...
Representation theory of affine superalgebras at the critical level.