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.
Defining relations for classical Lie superalgebras without Cartan matrices.
Dimensions of Demazure modules for rank two affine Lie algebras
Elliptic genera and the moonshine module.
Epsilon systems on geometric crystals of type .
Équations de Knizhnik-Zamolodchikov et théorie des représentations
Explicit description of a family of affine Kac-Moody groups. (Description explicite d'une famille de groupes de Kac-Moody affines.)
Fusion algebras for superconformal field theories through coinvariants. II: super-Virasoro-symmetry.
Generalized Kac-Moody algebras and the modular function j.
Generating operator of or Gaudin transfer matrices has quasi-exponential kernel.
Groupes associés aux algèbres de Kac-Moody
Homogeneous representations of Khovanov–Lauda Algebras
We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.