Typical representations via fixed point sets in BruhatTits buildings
Abstract
For an essentially tame supercuspidal representation $\pi$ of a connected reductive $p$adic group $G$, we establish two distinct and complementary sufficient conditions for the irreducible components of its restriction to a maximal compact subgroup to occur in a representation of $G$ which is not inertially equivalent to $\pi$. These two results are further formulated in terms of the geometry of the BruhatTits building of $G$ and its fixed points under the action of certain tori. The consequence is a set of broadly applicable tools for addressing the branching rules of $\pi$ and the unicity of $[G,\pi]_G$types.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.05895
 Bibcode:
 2019arXiv190905895L
 Keywords:

 Mathematics  Representation Theory;
 22E50
 EPrint:
 33 pages. Substantial changes from previous versions