Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms

2004/08/03 by Jens Funke, John Millson, John J. Millson +2 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Finite Group Theory Research #math.NT #math.RT #msc:11F27 #msc:11F46 #msc:22E40

paper · pdf · doi:10.48550/arxiv.math/0408050

arxiv created 2004/08/03 · arxiv updated 2009/12/01

Abstract

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. We generalize the Kudla-Millson relation between intersection numbers of cycles and Fourier coefficients of Siegel modular forms to the case where the cycles have local coefficients. Now the generating series of the cycles give rise to vector-valued Siegel modular forms. The underlying correspondence between the highest weights of the orthogonal and the symplectic group coincides with the one obtained by Adams for which we provide a geometric interpretation.

Citations

• On modular forms associated with indefinite quadratic forms of signature (2,n?2)

Cited by

• Jacobi Forms of Affine Weight in Higher Cogenus and Nearly Holomorphic Functions

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