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Some subregular germs for \(p\)-adic \(Sp_ 4(F)\). (English) Zbl 0837.22007

The Shalika germ expansion [J. Shalika, Ann. Math., II. Ser. 95, 226-242 (1972; Zbl 0281.22011)] expresses semisimple orbital integrals on \(p\)-adic reductive groups in terms of unipotent ones and some universal germs. It has become an important tool in \(p\)-adic harmonic analysis, especially in applications of the trace formula.
In the present paper the authors give explicit computations of some subregular germs in the group \(G= Sp_4(F)\) for a \(p\)-adic field \(F\).

MSC:

22E35 Analysis on \(p\)-adic Lie groups
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)

Citations:

Zbl 0281.22011
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