$\mathbb{P}\mathfrak{gl}_{2}$ is Multiplicity-Free as a $PGL_{2} \times PGL_{2}$-Variety

Dmitry Gourevitch; Shai Keidar

paper

$P gl_{2}$ is Multiplicity-Free as a $P G L_{2} \times P G L_{2}$ -Variety

arXiv:1912.04997

Abstract

Let $F$ be a non-Archimedean local field. Let $G$ be an algebraic group over $F$ . A $G$ -variety $X$ defined over $F$ is said to be multiplicity-free if for any admissible irreducible representation $π$ of $G (F)$ the following takes place: $dim H o m_{G (F)} (S (X (F)), π) \leq 1$ where $S (X (F))$ is the space of Schwartz functions on $X (F)$ . In this thesis we prove that $P gl_{2} (F)$ is multiplicity-free as a $P G L_{2} (F) \times P G L_{2} (F)$ -variety.

MSc thesis completed at Weizmann Institute of Science under the guidance of Prof. Dmitry Gourevitch

References in corpus (1)

Harmonic analysis on real reductive symmetric spaces

Pgl2​ is Multiplicity-Free as a PGL2​×PGL2​-Variety

Abstract

References in corpus (1)

$P gl_{2}$ is Multiplicity-Free as a $P G L_{2} \times P G L_{2}$ -Variety