By Colette Mœglin, Marie-France Vignéras, Jean-Loup Waldspurger (auth.)
This booklet grew out of seminar held on the collage of Paris 7 through the educational yr 1985-86. the purpose of the seminar used to be to provide an exposition of the idea of the Metaplectic illustration (or Weil illustration) over a p-adic box. The e-book starts with the algebraic concept of symplectic and unitary areas and a common presentation of metaplectic representations. It maintains with exposés at the fresh paintings of Kudla (Howe Conjecture and induction) and of Howe (proof of the conjecture within the unramified case, representations of low rank). those lecture notes comprise numerous unique effects. The ebook assumes a few heritage in geometry and mathematics (symplectic kinds, quadratic types, reductive teams, etc.), and with the speculation of reductive teams over a p-adic box. it really is written for researchers in p-adic reductive teams, together with quantity theorists with an curiosity within the function performed through the Weil illustration and -series within the idea of automorphic forms.
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Extra info for Correspondances de Howe sur un corps p-adique
ZELEVINSKI, Representations of the group GL(n,F) where F is a non archimedean local field, Russian Math. Surveys 31 (1976), 1-68. FLATH, Decomposition of representations into tensor products, in Automorphic forms, representations and L-functions, Proc. Symp. in Pure Math. XXXIII, AMS 1979, 179-184. HOWE, ~-series and invariant theory, in Automorphic forms, representations and L-functions, Proc. Symp. in Pure Math. XXXIII, AMS 1979, 275-286. HOWE, Transcending classical invariant theory, preprint.
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48 Conjecture. S i F est local non archim~dien, V 2'' __deV~, invariant par il existe un unique sous-espace , tel que V2/V 2 soit irr~ductible. Si cette assertion est vraie, on note V2-V2/V 2, ~ 2 la representation de H 2 dans V 2. On dit que ~2 correspond g ~ l . Remarques. 2. 6, et au chap. 17, si la conjecture est vraie pour toute paire r~ductive duale irr~ductible, elle est vraie pour toute paire r~ductive duale. 2. ). (4) L'analogue pour F = ~ a 4t~ d4montr~ par Howe ([H2]). (5) L'analogue de la conjecture pour F fini est faux (voir [H3]).
Correspondances de Howe sur un corps p-adique by Colette Mœglin, Marie-France Vignéras, Jean-Loup Waldspurger (auth.)