The Integral on Quantum Super Groups of Type $A_{r|s}$

Non-commutative matrix integrals and representation varieties of surface groups in a finite group

A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Moebius graphs. The contribution of each graph is an invariant of the topological type of the surface on which the graph is drawn. As an example, we calculate the integral on the group algebra of a finite group. We show that the integral is a generating function of the number of homomorphisms from the fundamental group of an arbitrary closed surface into the finite group. The …

Path Integral Quantization of the Symplectic Leaves of the SU(2)* Poisson-Lie Group

The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations and also compare the results with the path integral quantization of spin.

Addendum to the paper "Combinatorics of the modular group II: the Kontsevich integrals"

Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)

Integrals on Hopf algebras and Application to Representation Theory of Quantum Groups of Type $A_{0|0}$

In this work we study some properties of comldules over (non-cosemisimple) Hopf algebras possessing integrals, which are also called co-Frobenius Hopf algebras. We apply the result obtained to the classification of representations of quantum groups of type $A_{0|0}$.

Extended affine Weyl groups: Presentation by conjugation via integral collection

We give several necessary and sufficient conditions for the existence of {\it the presentation by conjugation} for a non-simply laced extended affine Weyl group. We invent a computational tool by which one can determine simply the existence of the presentation by conjugation for an extended affine Weyl group. As an application, we determine the existence of the presentation by conjugation for a large class of extended affine Weyl groups.

某些积分非退化融合范畴的群论性质

Group-theoretical property of some integral non-degenerate fusion categories

本文证明，若积分非退化融合范畴的简单对象的Frobenius-Perron维数均为1或素数p的幂，则该范畴是群论的。