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Irreducibility and Cuspidality

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Representation Theory and Automorphic Forms

Part of the book series: Progress in Mathematics ((PM,volume 255))

Summary

Suppose ρ is an n-dimensional representation of the absolute Galois group of Q which is associated, via an identity of L-functions, with an automorphic representation π of GL(n) of the adele ring of Q. It is expected that π is cuspidal if and only if ρ is irreducible, though nothing much is known in either direction in dimensions > 2. The object of this article is to show for n < 6 that the cuspidality of a regular algebraic π is implied by the irreducibility of ρ. For n < 5, it suffices to assume that π is semi-regular.

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Authors and Affiliations

  1. 253-37 Caltech, Pasadena, CA 91125, USA

    Dinakar Ramakrishnan

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  1. Dinakar Ramakrishnan
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Editors and Affiliations

  1. RIMS, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

    Toshiyuki Kobayashi

  2. Department of Mathematics, Harvard University, Cambridge, MA 02138, U.S.A

    Wilfried Schmid

  3. Department of Mathematics, Inha University, Incheon 402-751, Republic of Korea

    Jae-Hyun Yang

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Ramakrishnan, D. (2008). Irreducibility and Cuspidality. In: Kobayashi, T., Schmid, W., Yang, JH. (eds) Representation Theory and Automorphic Forms. Progress in Mathematics, vol 255. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4646-2_1

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