A simple construction of stein’s complementary series representations

TY - JOUR

T1 - A simple construction of stein’s complementary series representations

AU - Sahi, Siddhartha

PY - 1990/1

Y1 - 1990/1

N2 - We given an elementary construction of Stein’s complementary series for GL(2n) over an arbitrary local field F, and determine their restrictions to the “mirabolic” subgroup P2n ≈ GL(2n − 1, F)∝F2n − 1. Taken together with the results in [S], this allows one to calculate the adduced representation An for an arbitrary irreducible, unitary representation Σ of GL(n, C).

AB - We given an elementary construction of Stein’s complementary series for GL(2n) over an arbitrary local field F, and determine their restrictions to the “mirabolic” subgroup P2n ≈ GL(2n − 1, F)∝F2n − 1. Taken together with the results in [S], this allows one to calculate the adduced representation An for an arbitrary irreducible, unitary representation Σ of GL(n, C).

KW - Adduced representation

KW - Stein’s complementary series

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U2 - https://doi.org/10.1090/S0002-9939-1990-0984813-7

DO - https://doi.org/10.1090/S0002-9939-1990-0984813-7

M3 - Article

SN - 0002-9939

VL - 108

SP - 257

EP - 266

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -