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The Abelian–Nonabelian Correspondence for I -Functions

Rachel Webb

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Source: Crossref

Published: Nov 20, 2021

DOI: 10.1093/imrn/rnab305

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Source abstract

Abstract We prove the abelian–nonabelian correspondence for quasimap II-functions. That is, if ZZ is an affine l.c.i. variety with an action by a complex reductive group GG, we prove an explicit formula relating the quasimap II-functions of the geometric invariant theory quotients Z//θGZ\mathord{/\mkern -6mu/}_{\theta } G and Z//θTZ\mathord{/\mkern -6mu/}_{\theta } T where TT is a maximal torus of GG. We apply the formula to compute the JJ-functions of some Grassmannian bundles on Grassmannian varieties and Calabi–Yau hypersurfaces in them.

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