A character approach to Looijenga's invariant theory for generalized root systems
A construction of some ideals in affine vertex algebras.
A Hyperbolic Kac-Moody Algebra and the Theory of Siegel Modular Forms of Genus 2.
A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras.
Algebraic loop groups and moduli spaces of bundles
We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.
Almost-graded central extensions of Lax operator algebras
Lax operator algebras constitute a new class of infinite dimensional Lie algebras of geometric origin. More precisely, they are algebras of matrices whose entries are meromorphic functions on a compact Riemann surface. They generalize classical current algebras and current algebras of Krichever-Novikov type. Lax operators for 𝔤𝔩(n), with the spectral parameter on a Riemann surface, were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structure was revealed and...
An equivalence between categories of modules for generalized Kac-Moody Lie algebras.
An Equivalence of Fusion Categories.
Arrangements of hyperplanes and Lie algebra homology.
Automorphic forms on Os + 2,2(R) and infinte products.
Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras.
Bigèbres de Lie, doubles et carrés
Categories of nonstandard highest weight modules for affine Lie algebras.
Classification des algèbres de Lie graduées simples de croissance ... 1.
Classification of Loop Modules with finite dimensional weight spaces.
Classification of simple graded Lie algebras of finite growth.
Cohomologie T-équivariante de la variété de drapeaux d'un groupe de Kač-Moody
Cohomology Groups of Infinite Dimensional Algebras.
Coloured generalised Young diagrams for affine Weyl-Coxeter groups.
Combinatorial bases of modules for affine Lie algebra B 2(1)
We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases...