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Elliptic genera of homogeneous spin manifolds and theta functions identities. (English) Zbl 1217.58015
Summary: By the Witten rigidity theorem and the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, the elliptic genus of a homogeneous spin manifold \(G/H\) can be expressed as a sum of theta functions quotients over the Weyl group of \(G\). Consequently, we obtain several classes of combinatorial identities of theta functions.

MSC:
58J26 Elliptic genera
11F27 Theta series; Weil representation; theta correspondences
58J20 Index theory and related fixed-point theorems on manifolds
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