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Representations of $p$-adic symplectic groups

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Representations of p-adic symplectic groups COMPOSITIO MATHEMATICA MARKO TADIC´ Representations of p-adic symplectic groups Compositio Mathematica, tome 90, no 2 (1994), p. 123-181. <> © Foundation Compositio Mathematica, 1994, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: // implique l’accord avec les conditions gé- nérales d’utilisation ( Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques 123 Representations of p-Adic Symplectic Groups MARKO TADI0106 Department of Mathematics, University of Zagreb, Bijenicka 30, 41000 Zagreb, Croatia Current address: Sonderforschungsbereich 170, Geometrie &#x26; Analysis, Bunsenstr. 3-5, 37073 Gottingen, Germany Received 1 May 1991; received in final form 8 December 1992 Compositio Mathematica 90: 123-181, 1994. (Ç) 1994 Kluwer Academic Publishers. Printed in the Netherlands. 0. Introduction A non-archimedean field of a characteristic different from two is denoted by F. In this paper we consider the representation theory of groups Sp(n, F) and GSp(n, F). The inner geometry of these groups motivates us to consider the representations of these groups as modules over representations of general linear groups. Such an idea goes back to D. K. Faddeev in the finite field case ([F]). D. Barbasch had also such point of view in [Ba]. Besides the module structure, we also have a comodule structure. Our motivation for such approach is to make symplectic case more close to the well understood theory of groups GL(n), as it was developed by J. Bernstein and A. V. Zelevinsky ([BnZl], [BnZ2], [Zl]), and to ideas developed in [Tl]. The bas

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