arXiv
Open Access
2018
Generic representations for symmetric spaces
Dipendra Prasad
Abstrak
For a connected quasi-split reductive algebraic group $G$ over a field $k$, which is either a finite field or a non-archimedean local field, $θ$ an involutive automorphism of $G$ over $k$, let $K =G^θ$. Let $K^1=[K^0,K^0]$, the commutator subgroup of $K^0$, the connected component of identity of $K$. In this paper, we provide a simple condition on $(G,θ)$ for there to be an irreducible admissible generic representations $π$ of $G$ with ${\rm Hom}_{K^1}[π,{\mathbb C}] \not = 0$. The condition is most easily stated in terms of a real reductive group $G_θ({\mathbb R})$ associated to the pair $(G,θ)$ being quasi-split.
Penulis (1)
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Dipendra Prasad
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2018
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓