The tempered spectrum of a real spherical space

TY - JOUR

T1 - The tempered spectrum of a real spherical space

AU - Knop, Friedrich

AU - Krötz, Bernhard

AU - Schlichtkrull, Henrik

PY - 2017/6

Y1 - 2017/6

N2 - Let G/H be a unimodular real spherical space which is either absolutely spherical, i.e. the real form of a complex spherical space, or of wave-front type. It is shown that every tempered representation for G/H embeds into a twisted discrete series for a boundary degeneration of G/H. If G/H is of wave-front type it follows that the tempered representation is parabolically induced by a twisted discrete series representation for a real spherical space formed by a Levi subgroup.

AB - Let G/H be a unimodular real spherical space which is either absolutely spherical, i.e. the real form of a complex spherical space, or of wave-front type. It is shown that every tempered representation for G/H embeds into a twisted discrete series for a boundary degeneration of G/H. If G/H is of wave-front type it follows that the tempered representation is parabolically induced by a twisted discrete series representation for a real spherical space formed by a Levi subgroup.

U2 - 10.4310/ACTA.2017.v218.n2.a3

DO - 10.4310/ACTA.2017.v218.n2.a3

M3 - Journal article

SN - 0001-5962

VL - 218

SP - 319

EP - 383

JO - Acta Mathematica

JF - Acta Mathematica

IS - 2

ER -