Kobayashi's conjecture on associated varieties for $({\mathrm{E}}_{6(-14)},\mathrm{Spin}(8,1))$

Abstract

The author confirms a conjecture on associated varieties by Toshiyuki KOBAYASHI for the Klein four symmetric pair $({\mathrm{E}}_{6(-14)},\mathrm{Spin}(8,1))$, which provides an alternative way to confirm the conjecture for the symmetric pair $(\mathrm{Spin}(8,2),\mathrm{Spin}(8,1))$. Also, for Klein four symmetric pairs $(G,G^{\Gamma })$ with the exceptional simple Lie groups $G$ of Hermitian type, there exists a discrete series representation of $G$ which is $G^{\Gamma }$-admissible if and only if $(G,G^{\Gamma })$ is of holomorphic type.

7 pages, 1 figure

References in corpus (2)

• Branching of some holomorphic representations of SO(2,N)
• Discrete branching laws for minimal holomorphic representations