By Colette Moeglin
This e-book grew out of seminar held on the college of Paris 7 through the educational 12 months 1985-86. the purpose of the seminar was once to provide an exposition of the speculation of the Metaplectic illustration (or Weil illustration) over a p-adic box. The ebook starts with the algebraic idea of symplectic and unitary areas and a basic 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 include numerous unique effects. The booklet assumes a few heritage in geometry and mathematics (symplectic types, quadratic varieties, reductive teams, etc.), and with the idea of reductive teams over a p-adic box. it's written for researchers in p-adic reductive teams, together with quantity theorists with an curiosity within the function performed via the Weil illustration and -series within the thought of automorphic varieties.
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