Abstract
We discuss generalized Bessel integrals with nondegenerate characters, which are assigned to irreducible submodules of a reducible degenerate principal series representation of Sp ( n , R ) . Then we give sufficient conditions for their vanishings which are based on the signatures of the nondegenerate characters. This consequently suggests a reasonable correspondence between open GL n ( R ) -orbits in the set of real symmetric matrices of size n and irreducible submodules of the reducible principal series representations.
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