Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Details Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

2009-09-16

arxiv.org/abs/0909.2999v1

Mathematics

Number Theory

112 pages

Scientific paper

We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel and Fourier-Jacobi models too. We formulate several conjectures about these restriction problems involving root numbers of symplectic representations in the local case, and central critical L-value in the global case. Along the way we prove several results both in number theory and representation theory.

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