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...
Combinatorial interpretations for rank-two cluster algebras of affine type.
Comments on the Links Between Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Conformal blocks and cohomology in genus 0
We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus for classical Lie algebras and .
Construction de formes automorphes réflectives sur un espace de dimension 4
Dans la lignée des travaux de V. Gritsenko et V. Nikulin, par des méthodes reliées aux formes de Jacobi définies relativement au réseau de racines on construit six formes automorphes réflectives qui seront associées à des algèbres de Kac–Moody hyperboliques de type de Borcherds, pour la signature et, pour quatre d’entre elles, on précisera une identité du type “formule du dénominateur”, déterminant entièrement l’algèbre en question.
Construction d'un groupe de Kac-Moody et applications
Coordinates of maximal roots of weakly non-negative unit forms
Critical points of the product of powers of linear functions and families of bases of singular vectors
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
We define the -restriction and -induction functors on the category of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.