6 D ec 1 99 9 AFFINE REPRESENTATIONS OF THE FUNDAMENTAL GROUP ( WITH AN APPENDIX ON PARABOLIC REPRESENTATIONS )

ar X iv : h ep - t h / 92 12 03 9 v 1 5 D ec 1 99 2 On Free Boson Representations of

A boson representation of the quantum affine algebra Uq(ŝl 2) is realized based on the Wakimoto construction. We discuss relations with the other boson representations.

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

Deformation of Outer Representations of Galois Group II

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...

ar X iv : f un ct - a n / 96 12 00 6 v 1 1 9 D ec 1 99 6 A CONNECTION BETWEEN MULTIRESOLUTION WAVELET THEORY OF SCALE N AND 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.