Lie Groups Seminar
Wednesday, November 28, 2018 at 4:30pm to 5:30pm
Monica Nevins (Ottawa)
On the unicity of types for supercuspidal representations
Types are representations of compact open subgroups which identify a Bernstein component of the category of smooth representations of a p-adic group G, by virtue of appearing in the restriction of each irreducible representation of that component and of no other. A construction of J. K. Yu gives types for supercuspidal representations; from these one can generate infinitely many more using G-conjugation and induction.
The conjecture of “unicity of types” is roughly: all types occur in this way. In this talk, we give a class of examples which disprove a stronger version of this conjecture (that types on maximal compact open subgroups are unique up to conjugacy). We nevertheless can prove the unicity conjecture for a large class of tame positive-depth supercuspidal representations of semisimple simply connected groups. This work in progress is joint with Peter Latham, King’s College, London.