On Branching Rules of Depth-Zero Representations
Abstract
Using Bruhat-Tits theory, we analyse the restriction of depth-zero representations of a semisimple simply connected -adic group to a maximal compact subgroup . We prove the coincidence of branching rules within classes of Deligne-Lusztig supercuspidal representations. Furthermore, we show that under obvious compatibility conditions, the restriction to of a Deligne-Lusztig supercuspidal representation of intertwines with the restriction of a depth-zero principal series representation in infinitely many distinct components of arbitrarily large depth. Several qualitative and quantitative results are obtained, and their use is illustrated in an example.
Cite
@article{arxiv.1302.5618,
title = {On Branching Rules of Depth-Zero Representations},
author = {Monica Nevins},
journal= {arXiv preprint arXiv:1302.5618},
year = {2014}
}
Comments
Final version: applications to bounds on GK-dimension added; deeper discussion conditions for coincidence of full branching rules of supercuspidals, final example corrected to include all three conjugacy classes of maximal tori