Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms
数论
2007-05-23 v1 表示论
摘要
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.
引用
@article{arxiv.math/0408050,
title = {Cycles with local coefficients for orthogonal groups and vector-valued Siegel modular forms},
author = {Jens Funke and John Millson},
journal= {arXiv preprint arXiv:math/0408050},
year = {2007}
}