2014/05/22 by Charlène Coniglio-Guilloton, Charlene Coniglio-Guilloton, Coniglio-Guilloton, Charlene
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1405.5638
in French
openalex publication_date 2014/05/22 · arxiv created 2014/06/02 · arxiv updated 2014/06/03 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Let K/F be a quadratic extension of non archimedean local fields. Let V be an irreducible level zero discrete series representation of the group G = GL2(R), where R is a division algebra of center K and of index r. One assumes that V is not a supercuspidal representation. Let D be a division algebra of center F and index 2r. In the following work, we try to answer this question : Is the representation V D*-distinguished if and only if its image by the Jacquet-Langlands correspondence is GL2(F)-distinguished. To answer this question, we use the coefficients system on the Bruhat-Tits building of G associated to the representation V by P. Schneider and U. Stuhler and the parametrization of level zero discrete series representation given by J. Silberger and E. W. Zink.