Integration over Compact Quantum Groups

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

ar X iv : m at h - ph / 9 91 20 06 v 1 7 D ec 1 99 9 Compact Quantum Groupoids

Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C *-algebras and Hilbert bimodules. The essential point is that whenever one has a tensor product over C in the theory of quantum groups, one now uses a certain tensor product over the base algebra of the quantum groupoid.

The Automorphic Membrane

We present a 1-loop toroidal membrane winding sum reproducing the conjectured M-theory, four-graviton, eight derivative, R amplitude. The U -duality and toroidal membrane world-volume modular groups appear as a Howe dual pair in a larger, exceptional, group. A detailed analysis is carried out for M-theory compactified on a 3-torus, where the target-space Sl(3,Z)× Sl(2,Z) U -duality and Sl(3,Z) ...

Discrete Hypergroups Associated with Compact Quantum Gelfand Pairs

A discrete DJS-hypergroup is constructed in connection with the linearization formula for the product of two spherical elements for a quantum Gelfand pair of two compact quantum groups. A similar construction is discussed for the case of a generalized quantum Gelfand pair, where the role of the quantum subgroup is taken over by a two-sided coideal in the dual Hopf algebra. The paper starts with...

Projective Techniques and Functional Integration for Gauge Theories

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used...