Given F a locally compact, nondiscrete, non-archimedean field of characteristic ≠ 2 and R an integral domain such that a non-trivial smooth character χ: F → R <sup>×</sup>exists, we construct the (reduced) metaplectic group attached to χ and R. We show that it is in the expected cases a double cover of the symplectic group over F. Finally, we define a faithful infinite dimensional R-representation of the metaplectic group analogue to the Weil representation in the complex case.

Chinello, G., Turchetti, D. (2015). Weil Representation and Metaplectic Groups over an Integral Domain. COMMUNICATIONS IN ALGEBRA, 43(6), 2388-2419 [10.1080/00927872.2014.893729].

Weil Representation and Metaplectic Groups over an Integral Domain

Chinello, Gianmarco
;
2015

Abstract

Given F a locally compact, nondiscrete, non-archimedean field of characteristic ≠ 2 and R an integral domain such that a non-trivial smooth character χ: F → R ×exists, we construct the (reduced) metaplectic group attached to χ and R. We show that it is in the expected cases a double cover of the symplectic group over F. Finally, we define a faithful infinite dimensional R-representation of the metaplectic group analogue to the Weil representation in the complex case.
Articolo in rivista - Articolo scientifico
Howe correspondence; Metaplectic group; Weil representation; l-modular representations;
Corrispondenza di Howe; gruppo metaplettico; rappresentazione di Weil; rappresentazioni l-modulari
English
2015
43
6
2388
2419
none
Chinello, G., Turchetti, D. (2015). Weil Representation and Metaplectic Groups over an Integral Domain. COMMUNICATIONS IN ALGEBRA, 43(6), 2388-2419 [10.1080/00927872.2014.893729].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/123549
Citazioni
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
Social impact