m at h . Q A ] 1 9 O ct 1 99 9 Actions of GL q ( 2 , C ) on C ( 1 , 3 ) and its four dimensional representations

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

We give a realization of crystal graphs for basic representations of the quantum affine algebra Uq(C (1) 2) in terms of new combinatorial objects called the Young walls.

ar X iv : m at h - ph / 9 91 00 13 v 1 8 O ct 1 99 9 q - deformed

Octahedral Galois Representations Arising from Q-curves of Degree 2

Generically, one can attach to a Q-curve C octahedral representations ρ : Gal(Q/Q) −→ GL 2 (F 3) coming from the Galois action on the 3-torsion of those abelian varieties of GL 2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations ρ having image into GL 2 (F 9). Going the other way, we ...

ar X iv : h ep - t h / 95 10 18 9 v 1 2 5 O ct 1 99 5 revised version q - Virasoro Operators from an Analogue of the Noether Currents 1

We discuss the q-Virasoro algebra based on the arguments of the Noether currents in a two-dimensional massless fermion theory as well as in a three-dimensional nonrelativistic one. Some notes on the q-differential operator realization and the central extension are also included.

/ 93 06 03 6 v 1 7 J un 1 99 3 Finite Dimensional Representations of U q ( C ( n + 1 ) ) at Arbitrary q

A method is developed to construct irreducible representations(irreps) of the quantum supergroup U q (C(n + 1)) in a systematic fashion. It is shown that every finite dimensional irrep of this quantum supergroup at generic q is a deformation of a finite dimensional irrep of its underlying Lie superalgebra C(n + 1), and is essentially uniquely characterized by a highest weight. The character of ...