Theta correspondence

In mathematics, the theta correspondence or Howe correspondence is a correspondence between automorphic forms associated to the two groups of a dual reductive pair, introduced by Howe (1979).

See also

Metaplectic group

References

Howe, Roger (1979), "θ-series and invariant theory", in Borel, Armand; Casselman, W., Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Providence, R.I.: American Mathematical Society, pp. 275–285, ISBN 978-0-8218-1435-2, MR 546602, http://www.ams.org/publications/online-books/pspum331-pspum331-ptII-8.pdf
Mœglin, Colette; Vignéras, Marie-France; Waldspurger, Jean-Loup (1987), Correspondances de Howe sur un corps p-adique, Lecture Notes in Mathematics, 1291, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0082712, ISBN 978-3-540-18699-1, MR 1041060
Waldspurger, Jean-Loup (1987), "Représentation métaplectique et conjectures de Howe", Astérisque, Séminaire Bourbaki 674 152-153: 85–99, ISSN 0303-1179, MR 936850, http://www.numdam.org/item?id=SB_1986-1987__29__85_0