Tensor products of finite and infinite dimensional representations of semisimple Lie algebras
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 arithmetic theory of loop groups
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The characteristic cycles of holonomic systems on a flag manifold.
The classification of Lie algebras with invariant cones.
The closure diagrams for nilpotent orbits of real forms of .
The closure diagrams for nilpotent orbits of real forms of and .
The combinatorics of orbital varieties closures of nilpotent order 2 in .
The duality correspondence of infinitesimal characters
We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.
The finite dimension property of the irreducible representations of Noetherian -Lie algebras.
The F-method and a branching problem for generalized Verma modules associated to
The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras , and generalized conformal -Verma modules of scalar type. As a result, we classify the -singular vectors for this class of -modules.
The geometry of nilpotent coadjoint orbits of convex type in hermitian Lie algebras.
The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.
The index of centralizers of elements of reductive Lie algebras.
The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties
The Khovanov-Lauda 2-category and categorifications of a level two quantum representation.
The Kostant partition functions for twisted Kac-Moody algebras.
The Lie algebra cohomology of jets.
The minimal orbit in a simple Lie algebra and its associated maximal ideal