Elliptic genera of homogeneous spin manifolds and theta functions identities. (English) Zbl 1217.58015

Song, Ruifang

Sci. China, Ser. A 48, No. 12, 1637-1645 (2005).

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

Keywords:

fixed point formula; Witten rigidity theorem; elliptic genus; Jacobi theta functions