Local theta correspondence and minimal \(K\)-types of positive depth (Q1425653)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Local theta correspondence and minimal \(K\)-types of positive depth |
scientific article; zbMATH DE number 2060065
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local theta correspondence and minimal \(K\)-types of positive depth |
scientific article; zbMATH DE number 2060065 |
Statements
Local theta correspondence and minimal \(K\)-types of positive depth (English)
0 references
17 March 2004
0 references
The following theorem is proved: two given irreducible admissible representations of positive depth which are paired in the theta correspondence for a reductive dual pair over a \(p\)-adic field have unrefined minimal \(K\)-types which are paired in the orbit correspondence. This theorem is applied to the theta correspondence for a dual pair of unitary groups.
0 references
irreducible admissible representation
0 references
positive depth
0 references
theta correspondence
0 references
orbit correspondence
0 references
Weil representation
0 references
Heisenberg group
0 references
unrefined minimal \(K\)-type
0 references
Cayley transform
0 references
unitary group
0 references
