R-group and Whittaker space of some genuine representations
Representation Theory
2021-07-01 v1 Number Theory
Abstract
For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such a principal series representation. Moreover, for saturated covers of a semisimple simply-connected group, we also propose a simpler conjectural formula for such dimensions. This latter conjectural formula is verified in several cases, including covers of the symplectic groups.
Keywords
Cite
@article{arxiv.1912.07408,
title = {R-group and Whittaker space of some genuine representations},
author = {Fan Gao},
journal= {arXiv preprint arXiv:1912.07408},
year = {2021}
}