Representations of forms of a Kac-Moody algebra. (Représentations des formes d'une algèbre de Kac-Moody.)
Rogers-Ramanujan identities: A century of progress from mathematics to physics.
Root vectors in quantum groups.
Rosso's form and quantized Kac Moody algebras.
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.
The 3-state Potts model and Rogers-Ramanujan series
We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra.
The classification of modular invariants revisited
The intertwining of affine Kac-Moody and current algebras
The Kostant partition functions for twisted Kac-Moody algebras.
The Lie algebra cohomology of jets.
The mathematics of fivebranes.
The triplet vertex operator superalgebras: twisted sector.