Representations of loop groups, Dirac operators on loop space, and modular forms

DOI10.1016/0040-9383(90)90016-DzbMath0715.22023OpenAlexW1964002331MaRDI QIDQ752204

Jean-Luc Brylinski

Publication date: 1990

Published in: Topology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0040-9383(90)90016-d

zbMATH Keywords

charactersDirac operatormodular formcongruence subgrouploop groupvector bundleindexcompact manifoldloop spaceelliptic cohomologyJacobi modular formsuniversal central extensionsmooth mapspositive energy representation

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Loop groups and related constructions, group-theoretic treatment (22E67) Exotic index theories on manifolds (58J22) Structure of modular groups and generalizations; arithmetic groups (11F06) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20)

Related Items (13)

Modular invariance and characteristic numbers ⋮ Rigidity of higher elliptic genera ⋮ Codes, vertex operators and topological modular forms ⋮ Exotic twisted equivariant K-theory ⋮ Toda brackets and congruences of modular forms ⋮ \(K(1)\)-local topological modular forms ⋮ Characteristic classes in $TMF$ of level $\Gamma _1(3)$ ⋮ The sigma orientation for analytic circle-equivariant elliptic cohomology ⋮ An algebraic description of the elliptic cohomology of classifying spaces ⋮ Semi-infinite Weil complex and the Virasoro algebra ⋮ Power operations in elliptic cohomology and representations of loop groups ⋮ On cobordism of manifolds with corners ⋮ The Dirac-Ramond operator on loops in flat space

This page was built for publication: Representations of loop groups, Dirac operators on loop space, and modular forms