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We consider N=4 theories on ALE spaces of $A_{k-1}$ type. As is well known, their partition functions coincide with $A_{k-1}$ affine characters. We show that these partition functions are equal to the generating functions of some peculiar classes of partitions which we introduce under the name orbifold partitions. These orbifold partitions turn out to be related to the generalized Frobenius partitions introduced by G. E. Andrews some years ago. We relate the orbifold partitions to the blended partitions and interpret explicitly in terms of a free fermion system.
We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric ${cal N}=2, 2^*$ gauge theories on ALE spaces of the $A_n$ type. Furthermore we d
We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d N=2 and 5d N=1 gauge theories for arbitrary g
We derive the classical type IIB supergravity solution describing fractional D3-branes transverse to a C^2/Gamma orbifold singularity, for Gamma any Kleinian ADE subgroup. This solution fully describes the N=2 gauge theory with appropriate gauge grou
We compute the prepotential for gauge theories descending from ${cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge
We investigate the classical geometry corresponding to a collection of fractional D3 branes in the orbifold limit of an ALE space. We discuss its interpretation in terms of the world-volume gauge theory on the branes, which is in general a non confor