Singular vectors corresponding to imaginary roots in verma modules over affine Lie algebras.
Smallness problem for quantum affine algebras and quiver varieties
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Spacelike singularities and hidden symmetries of gravity.
String functions for affine Lie algebras integrable modules.
Sugawara operators and Kac-Kazhdan conjecture.
Symmetries of the Kac-Peterson modular matrices of affine algebras.
Symplectic K2 of Laurent polynomials, associated Kac-Moody groups and Witt rings.
Systèmes de racines infinis
Systèmes hamiltoniens complètement intégrables et déformations d'algèbres de Lie.
Some of the completely integrable Hamiltonian systems obtained through Adler-Kostant-Symes theorem rely on two distinct Lie algebra structures on the same underlying vector space. We study here the cases when two structures are linked together by deformations.