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Vanishing of coefficients in overlapping germ expansions for $ p$-adic $ {\rm GL}(n)$

Authors: Fiona Murnaghan and Joe Repka
Journal: Proc. Amer. Math. Soc. 111 (1991), 1183-1193
MSC: Primary 22E35; Secondary 22E50
MathSciNet review: 1041010
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Abstract: Shalika germs at the identity in $ p$-adic $ {\text{GL}}(n)$ will blow up at other singular points. Waldspurger has developed a technique for describing this behaviour at intermediate singular points, giving a "germ expansion for germs". In this paper we discuss which germs occur in such an expansion and find that the answer is more complicated than expected.

References [Enhancements On Off] (What's this?)

  • [1] G. Lusztig, N. Spaltenstein, Induced unipotent classes, J. London Math. Soc. 19 (1979), 41-52. MR 527733 (82g:20070)
  • [2] F. Murnaghan, Invariant meromorphic distributions on $ p$-adic $ GL(n)$, Amer. J. Math. 111 (1989), 143-196. MR 980304 (90f:22016)
  • [3] J.-L. Waldspurger, Sur les germes de Shalika pour les groupes linéaires,, Math. Ann. 284 (1989), 199-221. MR 1000107 (91d:22016)
  • [4] A.V. Zelevinsky, Representations of finite classical groups, Lecture Notes in Math., vol. 869, Springer-Verlag, 1981. MR 643482 (83k:20017)

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Keywords: $ {\text{GL}}(n)$, reductive $ p$-adic group, germ expansion
Article copyright: © Copyright 1991 American Mathematical Society

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