Data:	Mercoledì 26 Maggio 2004, Ore 16.30
Luogo:	Aula 1201, Dip. Matematica, U. Roma "Tor Vergata"
Speaker:	Dr. Michael Müger, U. Amsterdam
Titolo:	CONFORMAL ORBIFOLD MODELS AND BRAIDED CROSSED G-CATEGORIES.
Abstract:	First, we show that a quantum field theory A living on the line and having a group G of inner symmetries gives rise to a category GLoc A of twisted representations. This category is a braided crossed G-category in the sense of Turaev. Its degree zero subcategory is braided and equivalent to the usual representation category Rep A. Secondly, we study the relation between GLoc A and the braided (in the usual sense) representation category Rep A^G of the orbifold theory A^G. We prove the equivalence Rep A^G = (GLoc A)^G, which is a rigorous implementation of the insight that one needs to take the twisted representations of A into account in order to determine Rep A^G. In the opposite direction we have GLoc A = Rep A^G \rtimes S, where S \subset Rep A^G is the full subcategory of representations of A^G contained in the vacuum representation of A, and \rtimes refers to my Galois extensions of braided tensor categories. In the particular case of a completely rational theory A and a finite group G this allows us to prove that A has g-twisted representations for every g in G, in fact the sum over the squared dimensions of the simple g-twisted representations is independent of g, thus equal to dim Rep A.