Mathematical Research Letters

Volume 25 (2018)

Number 6

Distinguished representations for $\mathrm{SL}(n)$

Pages: 1695 – 1717



U. K. Anandavardhanan (Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India)

Dipendra Prasad (School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India)


For $E/F$ a quadratic extension of local fields, and $\pi$ an irreducible admissible generic representation of $\mathrm{SL}_n (E)$, we calculate the dimension of $\mathrm{Hom}_{\mathrm{SL}_n (F)} [\pi,\mathbb{C}]$ and relate it to fibers of the base change map corresponding to base change of representations of $\mathrm{SU}_n (F)$ to $\mathrm{SL}_n (E)$ as suggested in [16]. We also deal with finite fields.

Received 3 December 2016

Accepted 7 August 2017

Published 25 March 2019