A unification of Knizhnik-Zamalodchikov and Dunkl operators via affine Hecke algebras.
Algèbres et équations non-linéaires
Arithmetic features of rational conformal field theory
Axiomatic analyticity properties and representations of particles in thermal quantum field theory
Boundary Liouville theory: Hamiltonian description and quantization.
Central extensions and stochastic processes associated with the Lie algebra of the renormalized higher powers of white noise
In the first part of the paper we discuss possible definitions of Fock representation of the *-Lie algebra of the Renormalized Higher Powers of White Noise (RHPWN). We propose one definition that avoids the no-go theorems and we show that the vacuum distribution of the analogue of the field operator for the n-th renormalized power of WN defines a continuous binomial process. In the second part of the paper we present without proof our recent results on the central extensions of RHPWN, its subalgebras...
Chern-Simons terms as an example of the relations between mathematics and physics
Comments on the Links Between Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
Complex cobordism ring and conformal field theory over Z.
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 .
Conformal blocks in the tensor product of vector representations and localization formulas
Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.
Conformal field theory
Construction of renormalized trajectory.
Critical points of the product of powers of linear functions and families of bases of singular vectors
Dimensional reduction of conformal tensors and Einstein-Weyl spaces.
Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere.
Elliptic cohomology
Équations de Knizhnik-Zamolodchikov et théorie des représentations
Examples of categorification
Factorization constraints and boundary conditions in rational CFT
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category 𝓒 with a distinguished object, a symmetric special Frobenius algebra A in 𝓒, via the so-called TFT-construction. These correlators satisfy in particular all factorization constraints, which involve gluing homomorphisms relating correlators of world sheets of different topology. We review the action...