2016/09/11 by Maxim Gurevich, Gurevich, Maxim, Jiajun Ma +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1609.03155
openalex publication_date 2016/09/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Let E/F be a quadratic extension of non-archimedean local fields of\ncharacteristic 0. In this paper, we investigate two approaches which attempt to\ndescribe the smooth irreducible representations of GL(n,E) that are\ndistinguished by its subgroup GL(n,F). One relates this class to\nrepresentations which come as base change lifts from a quasi-split unitary\ngroup F, while another deals with a certain symmetry condition. By\ncharacterizing the union of images of the base change maps we show that these\ntwo approaches are closely related. Using this observation, we are able to\nprove a statement relating base change and distinction for ladder\nrepresentations. We then produce a wide family of examples in which the\nsymmetry condition does not impose GL(n,F)-distinction, and thus exhibit the\nlimitations of these two approaches.\n