Theta correspondence

rdf:langString Theta correspondence

rdf:langString In mathematics, the theta correspondence or Howe correspondence is a mathematical relation between representations of two groups of a reductive dual pair. The local theta correspondence relates irreducible admissible representations over a local field, while the global theta correspondence relates irreducible automorphic representations over a global field. The theta correspondence was introduced by Roger Howe in . Its name arose due to its origin in André Weil's representation theoretical formulation of the theory of theta series in . The Shimura correspondence as constructed by Jean-Loup Waldspurger in and may be viewed as an instance of the theta correspondence.