TY - JOUR

T1 - Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method

AU - Szpruch Alpert, Daniel

PY - 2013/6

Y1 - 2013/6

N2 - Let Sp2n(F) be the metaplectic double cover of F where Sp2n(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 SO2n+1(F) is irreducible.

AB - Let Sp2n(F) be the metaplectic double cover of F where Sp2n(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 SO2n+1(F) is irreducible.

UR - http://www.scopus.com/inward/record.url?scp=84883790251&partnerID=8YFLogxK

U2 - 10.1007/s11856-012-0140-y

DO - 10.1007/s11856-012-0140-y

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84883790251

SN - 0021-2172

VL - 195

SP - 897

EP - 971

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -