naa a22 4500 510782876 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0140-y doi (NATIONALLICENCE)springer-10.1007/s11856-012-0140-y Szpruch Dani The Center for Advanced Studies in Mathematics, Ben Gurion University of the Negev, P.O.B. 653, 84105, Be'er Sheva, Israel aut Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method [Elektronische Daten] [Dani Szpruch] Let $$\overline {S{p_{2n}}({\rm{<Emphasis FontCategory="NonProportional">F</Emphasis>}})} $$ be the metaplectic double cover of F where F is a local field of characteristic 0. We use the Uniqueness of Whittaker model to define a metaplectic analog to Shahidi local coefficients and we use these coefficients to define gamma factors. We show that these gamma factors are multiplicative and satisfy the crude global functional equation. Then, we compute these factors in various cases and obtain explicit formulas for Plancherel measures. These computations are then used to prove some irreducibility theorems for parabolic induction on the metaplectic group over p-adic fields. In particular, we show that all principal series representations induced from unitary characters are irreducible. We also prove that parabolic induction from unitary supercuspidal representation of the Siegel parabolic sub group is irreducible if and only if a certain parabolic induction on F is irreducible. Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 897-971 0021-2172 195:2<897 2013 195 11856 https://doi.org/10.1007/s11856-012-0140-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0140-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Szpruch Dani The Center for Advanced Studies in Mathematics, Ben Gurion University of the Negev, P.O.B. 653, 84105, Be'er Sheva, Israel aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 897-971 0021-2172 195:2<897 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer