Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions

Abstract Let K be the compact Lie group USp ( N / 2 ) or SO ( N , R ) . Let M n K be the moduli space of framed K -instantons over S 4 with the instanton number n . By Donaldson (1984), M n K is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ − 1 ( 0 ) , where μ is a holomorphic moment map such that μ − 1 ( 0 ) consists of the ADHM data. The purpose of the paper is to study the geometric properties of μ − 1 ( 0 ) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K = USp ( N / 2 ) then μ is flat and μ − 1 ( 0 ) is an irreducible normal variety for any n and even N . If K = SO ( N , R ) the similar results are proven for low n and N . As an application one can obtain a mathematical interpretation of the K -theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).