A note on the multiplicity of SL(n) over function fields

2018/10/28 by An, Yang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.11752

Abstract

In \citelafforgue2012chtoucas, Vicent Lafforgue attaches a semisimple Langlands parameter (or, what amounts to the same thing, a G-pseudocharacter) to every cuspidal automorphic representation of a reductive group G over the field of functions of a smooth projective algebraic curve X over a finite field. Hence, gets a decomposition of the space of cusp forms. In this note, we show that in the case of G = SL(n), Lafforgue's decomposition coincides with the classical decomposition using L-packets, and moreover, the number of (G-equivalence classes of) extensions of an unramified Hecke character of G to G-pseudocharacters serves as a natural upper bound on the multiplicity of SL(n).

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