TY - JOUR
T1 - On Bessel integrals for reducible degenerate principal series representations
AU - Miyazaki, Takuya
PY - 2011/5/1
Y1 - 2011/5/1
N2 - 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 GLn(R)-orbits in the set of real symmetric matrices of size n and irreducible submodules of the reducible principal series representations.
AB - 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 GLn(R)-orbits in the set of real symmetric matrices of size n and irreducible submodules of the reducible principal series representations.
KW - Degenerate principal series representations
KW - Generalized Bessel integrals
KW - Generalized confluent hypergeometric functions
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U2 - 10.1016/j.jfa.2011.01.013
DO - 10.1016/j.jfa.2011.01.013
M3 - Article
AN - SCOPUS:79951579690
VL - 260
SP - 2579
EP - 2597
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 9
ER -