This Licentiate Thesis contains the following papers: 1. Ernst T., Silvestrov SD: Shift
difference equations, symmetric polynomials and representations of the symmetric group …

We introduce a general notion of quantum universal envelo** algebroids (QUE
algebroids), or quantum groupoids, as a unification of quantum groups and star-products …

The classical Yang–Baxter equation (CYBE) is an algebraic equation central in the theory of
integrable systems. Its nondegenerate solutions were classified by Belavin and Drinfeld …

This paper arose from a minicourse given by the first author at MIT in the Spring of 1999,
when the second author extended and improved his lecture notes of this minicourse. It …

We describe representation theory of the elliptic quantum group E τ, η (sl 2). It turns out that
the representation theory is parallel to the representation theory of the Yangian Y (sl 2) and …

We consider a CPT-noninvariant scalar model and a modified version of quantum
electrodynamics with an additional photonic Chern–Simons-like term in the action. In both …

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference
operators acting on functions on the type A weight space. According to the fundamental …

arxiv:q-alg/9712037v1 12 Dec 1997 Page 1 arxiv:q-alg/9712037v1 12 Dec 1997 Universal
Solutions of Quantum Dynamical Yang–Baxter Equations D. Arnaudon∗ Laboratoire de …

We consider the universal solution of the Gervais-Neveu-Felder equation in the Uq (sl2)
case. We show that it has a quasi-Hopf algebra interpretation. We also recall its relation to …

We discuss supersymmetric Yang-Mills theories with multiple scales in the brane language.
The issue concerns N= 2 SUSY gauge theories with massive fundamental matter including …