Conservation relations for local theta correspondence

By Binyong Sun, Chengru Zhu. 2012

89 citations recorded by the source corpus.

We prove Kudla-Rallis conjecture on first occurrences of local theta correspondence, for all type I irreducible dual pairs and all local fields of characteristic zero.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/acb9b5c53435d38fcc3241c3352b3e87792e5c72

Citations in the corpus

• Local theta correspondence of tempered representations and Langlands parameters (2016, unknown): “′ = (V′ m). We shall denote the two Witt towers by (V+ m) and (V− m) and denote the first occurrence indices of πby m±(π) accordingly. The conservation relation, shown by Kudla–Rallis [KR] and Sun–Zhu [SZ], says that m+(π) +m−(π) = 2·(n+ǫ0 +1). This shows that mdown(π) = min{m+(π),m−(π)}≤n+ǫ0 +1 and ”