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Some results on multiplicities for SL(n)

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Abstract

We define the multiplicity and the global multiplicity of anL-packet of SL(n), unifying lack of multiplicity one and non-rigidity ofL-packets. The first examples of these phenomena were given by Blasius. Giving a heuristic approach to its calculation, based on Langlands’ Tannakian formalism, we conjecture that the global multiplicity is bounded in terms ofn only. We justify the heuristics in a special case ofL-packets attached to Hecke characters on an Abelian orp-extension. We then focus onL-packets lifted from endoscopic tori. A full description of their global multiplicities is given in the case wheren is prime.

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  1. Erez M. Lapid

    Present address: School of Mathematics, Institute for Advanced Study, 08540, Princeton, NJ, USA

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  1. Faculty of Mathematical Sciences, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Erez M. Lapid

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Lapid, E.M. Some results on multiplicities for SL(n). Isr. J. Math. 112, 157–186 (1999). https://doi.org/10.1007/BF02773481

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  • DOI: https://doi.org/10.1007/BF02773481

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