ar X iv : m at h / 99 11 07 4 v 1 [ m at h . Q A ] 1 1 N ov 1 99 9 CRYSTAL GRAPHS FOR BASIC REPRESENTATIONS OF THE QUANTUM AFFINE

ar X iv : m at h / 99 11 10 9 v 1 [ m at h . R A ] 1 5 N ov 1 99 9 – 1 – BIRKHOFF ’ S THEOREM FOR PANSTOCHASTIC MATRICES

The panstochastic analogue of Birkhoff's Theorem on doubly-stochastic matrices is proved in the case n = 5. It is shown that this analogue fails when n > 1, n = 5.

ar X iv : h ep - t h / 94 10 11 8 v 2 2 2 N ov 1 99 4 WILSON LOOPS , qq̄ and 3 q POTENTIALS , BETHE – SALPETER EQUATION

ar X iv : m at h / 99 11 14 3 v 1 [ m at h . D S ] 1 8 N ov 1 99 9 CANONICAL SYMBOLIC DYNAMICS FOR ONE - DIMENSIONAL GENERALIZED SOLENOIDS

We define canonical subshift of finite type cover for Williams' 1-dimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.

ar X iv : h ep - t h / 94 11 03 9 v 1 5 N ov 1 99 4 DFTT - 44 / 94 November 1994 R - MATRIX FORMULATION OF THE QUANTUM INHOMOGENEOUS GROUPS

ar X iv : m at h / 99 03 18 1 v 1 [ m at h . A G ] 3 0 M ar 1 99 9 PARABOLIC SHEAVES ON SURFACES AND AFFINE LIE ALGEBRA