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Dec 22, 2009 at 19:47 comment added S. Carnahan By "lives on" I mean sheaves on G/G have a convolution operation from the E[2] structure of G/G, and one can construct the quantum double as sections of a sheaf on G/G together with an E[2] multiplication map using the convolution. I don't have a precise reference, since I worked it out while trying to understand some writing by Majid about transmutation. In the finite case, there is some information in Willerton: 0503.5266. I think Ben-Zvi-Francis-Nadler may have some rough sketches in more general contexts.
Dec 18, 2009 at 20:38 comment added Mariano Suárez-Álvarez Scott, can you make precise and/or provide references for your statement that "the quantum double lives on the two-fold loop space"?
Oct 26, 2009 at 9:08 history answered S. Carnahan CC BY-SA 2.5