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Elliptic genera of homogeneous spin manifolds and theta functions identities

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Abstract

By 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.

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  1. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

    Song Ruifang

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  1. Song Ruifang
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Correspondence to Song Ruifang.

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Ruifang, S. Elliptic genera of homogeneous spin manifolds and theta functions identities. Sci. China Ser. A-Math. 48, 1637–1645 (2005). https://doi.org/10.1360/022005-50

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