Ja n 20 04 ALGEBRAS OF MINORS

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

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

We describe explicitly the algebras of degree zero operations in connective and periodic p-local complex K-theory. Operations are written uniquely in terms of certain infinite linear combinations of Adams operations, and we give formulas for the product and coproduct structure maps. It is shown that these rings of operations are not Noetherian. Versions of the results are provided for the Adams...

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 3 Ja n 20 04 Affine braids , Markov traces and the category

This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi type identities, dual pairs [Ze], and link invariants [Tu2]. The key observation in the genesis of this paper was that the technical tools used to obtain the results in Orellana [Or] and Suzuki [Su], t...

Ja n 20 04 q - LÉVY PROCESSES

We continue the investigation of the Lévy processes on a q-deformed full Fock space started in [1]. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a chaotic representation property for it in terms of multiple integrals with respect to diagonal measures, in the style of Nualart and Schoutens. We define stochas-tic int...