Generalized twisted quantum doubles of a finite group and rational orbifolds

Braid Group Representations from Twisted Quantum Doubles of Finite Groups

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite groups, in contrast to the categories associated with quantum groups at roots of unity. We also show that in the case of p-groups, the corresponding pure br...

Twisted quantum doubles

Group Cohomology and Gauge Equivalence of Some Twisted Quantum Doubles

We study the module category associated to the quantum double of a finite abelian group G twisted by a 3-cocycle, which is known to be a braided monoidal category, and investigate the question of when two such categories are equivalent. We base our discussion on an exact sequence which interweaves the ordinary and Eilenberg-Mac Lane cohomology of G. Roughly speaking, this reveals that the data ...

Generalized Twisted Sectors of Orbifolds

For a finitely generated discrete group Γ, the Γ-sectors of an orb-ifold Q are a disjoint union of orbifolds corresponding to homomorphisms from Γ into a groupoid presenting Q. Here, we show that the inertia orbifold and k-multi-sectors are special cases of the Γ-sectors, and that the Γ-sectors are orbifold covers of Leida's fixed-point sectors. In the case of a global quotient, we show that th...

Orbifolds and Finite Group Representations

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian group Ar (n) for A-type hypersurface quotient singularity of dimension n is introduced. For n = 4, the structure of Hilbert scheme of group orbits and crepant resolutions of Ar (4)-singularit...