2 9 Ja n 20 04 ALGEBRAS OF OPERATIONS IN K - THEORY

ar X iv : m at h / 04 01 23 7 v 1 [ m at h . C O ] 1 9 Ja n 20 04 1 Enumerative properties of generalized associahedra

Some enumerative aspects of the fans, called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras are considered, in relation with a bicomplex and its two spectral sequences. A precise enumerative relation with the lattices of generalized noncrossing partitions is conjectured and some evidence is given.

2 7 Ja n 20 04 Representations of trigonometric Cherednik algebras of rank 1 in positive characteristic Frédéric Latour

Ja n 20 04 ALGEBRAS OF MINORS

To Jürgen Herzog on the occasion of his 60th birthday

/ 02 01 23 9 v 1 2 9 Ja n 20 02 Boundary conditions in charge conjugate sl ( N ) WZW theories

We compute the representations (" nim-reps ") of the fusion algebra of sl(N) which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general validity, the other specific to the problem at hand. The problem is related to the classical problem of decomposition of the fundamental representations of sl(N) onto re...

0 v 1 1 2 Ja n 20 04 Closed relativistic string carrying pointlike mass

For the closed relativistic string carrying a pointlike mass the exact solutions of the dynamical equations are obtained and studied. These solutions describe states of the mentioned system moving in Minkowski space and also in the space that is the direct product of Minkowski space and a compact manifold (torus). We consider the closed relativistic string with one massive point (homeomorphic t...