2009/09/01 by Joshua M. Lansky, Lansky, Joshua M., C. Ryan Vinroot +1
Mathematics · #22E50 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:22E50
paper · pdf · doi:10.48550/arxiv.0909.0155
8 pages
arxiv created 2009/09/01 · arxiv updated 2009/12/01
We study Klyachko models of \rm SL(n, F), where F is a nonarchimedean local field. In particular, using results of Klyachko models for \rm GL(n, F) due to Heumos, Rallis, Offen and Sayag, we give statements of existence, uniqueness, and disjointness of Klyachko models for admissible representations of \rm SL(n, F), where the uniqueness and disjointness are up to specified conjugacy of the inducing character, and the existence is for unitarizable representations in the case F has characteristic 0. We apply these results to relate the size of an L-packet containing a given representation of \rm SL(n, F) to the type of its Klyachko model, and we describe when a self-dual unitarizable representation of \rm SL(n, F) is orthogonal and when it is symplectic.