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## Seminars

### A counterexample to a Q-series analogue of Casselman’s subrepresentation theorem

- Hold Date
- 2021-07-12 17:00〜2021-07-12 18:00
- Place
- Zoom
- Object person
- Speaker
- Taito Tauchi (IMI Kyushu University, JSPS-PD)

Abstract

Let G be a real reductive Lie group, Q a parabolic subgroup of G, and π an irreducible admissible representation of G. We say that π belongs to Q-series if it occurs as a subquotient of some degenerate principal series representation induced from Q. Then, any irreducible admissible representation belongs to P-series by Harish-Chandra’s subquotient theorem, where P is a minimal parabolic subgroup of G. On the other hand, Casselman’s subrepresentation theorem implies any representation belonging to P-series can be realized as a subrepresentation of some principal series representation induced from P. In this talk, we discuss a counterexample to a Q-series analogue of this subrepresentation theorem. More precisely, we show that there exists an irreducible admissible representation belonging to Q-series, which can not be realized as a subrepresentation of any degenerate principal series representation induced from Q.