N ov 2 00 2 TOPOLOGY OF U ( 2 , 1 ) REPRESENTATION SPACES

N ov 2 00 7 Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of

Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...

N ov 2 00 4 Notes on Stein - Sahi representations and some problems of non L 2 harmonic analysis Neretin

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces. Recently, Oshima [67] published his formula for c-function for L 2 on pseudo-Riemannian symmetric spaces (see also works of Delorm [12] and van den Ban– Schlichtkrull [3], [4]). After this, there arises a natural question about other solvable problems of non-commutative harmonic analysis. In the Appendix to the paper...

N ov 2 00 6 A Combination Theorem for Strong Relative Hyperbolicity Mahan

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups.

ar X iv : m at h . R T / 0 11 13 06 v 1 2 9 N ov 2 00 1 CARTAN DETERMINANTS AND SHAPOVALOV FORMS

We compute the determinant of the Gram matrix of the Shapovalov form on weight spaces of the basic representation of an affine Kac-Moody algebra of ADE type (possibly twisted). As a consequence, we obtain explicit formulae for the determinants of the Cartan matrices of p-blocks of the symmetric group and its double cover, and of the associated Hecke algebras at roots of unity.

2 8 N ov 2 00 5 Moduli spaces of local systems and higher Teichmüller theory