Part of the Lecture Notes in Mathematics book series (LNM, volume 114)
KeywordsIrreducible Representation Invariant Subspace Haar Measure Cartan Subgroup Finite Dimensional Space
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References for Chapter I
The Weil representation is constructed in
- 1.Weil, A., Sur certains groupes d'opérateurs unitaires, Acta Math., t. 111, 1964.Google Scholar
One of the first to study representations of groups over non-archimedean local fields was F. Mautner in
- 2.Mautner, F., Spherical functions over g — adic fields, I, Amer. Jour. Math., vol LXXX, 1958.Google Scholar
Absolutely cuspidal representations were first constucted by Gelfand and Graev. References to their work and that of Kirillov will be found in
- 3.Gelfand, I.M., M.I. Graev, and I.I. Pyatetskii — Shapiro, Representation Theory and Automorphic Functions, W.B. Saunders Co., 1966.Google Scholar
These representations were constructed in terms of the Weil representation by Shalika and by Tanaka.
To classify the representations over an archimedean field we have used a theorem of Harish-Chandra which may be found in
- 6.Harish-Chandra, Representations of semisimple Lie groups, II, T.A.M.S., vol 76, 1954.Google Scholar
Our discussion of characters owes much to
- 7.Sally, P.J. and J.A. Shalika, Characters of the discrete series of representations of SL(2) over a local field, P.N.A.S., 1968.Google Scholar
Three standard references to the theory of L — functions are
In Paragraph 8 we have used a result from
- 11.Harish-Chandra, Automorphic forms on semisimple Lie groups, Springer-Verlag, 1968.Google Scholar
Tamagawa measures are discussed in
- 12.Weil, A. Adèles and algebraic groups, Institute for Advanced Study, 1961.Google Scholar
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