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A two dimensional gauge theory is canonically associated to every Drinfelddouble. For particular doubles, the theory turns out to be e.g. the ordinaryYang-Mills theory, the G/G gauged WZNW model or the Poisson $\sigma$-model thatunderlies the Kontsevich quantization formula. We calculate the arbitrary genuspartition function of the latter. The result is the $q$-deformation of theordinary Yang-Mills partition function in the sense that the series over theweights is replaced by the same series over the $q$-weights. For $q$ equal to aroot of unity the series acquires the affine Weyl symmetry and its truncationto the alcove coincides with the Verlinde formula.Comment: 36 pages, LaTeX, references adde

The Formulae of Kontsevich and Verlinde¶from the Perspective of the Drinfeld Double