Analytic Representation Theory of Lie Groups: General Theory and Analytic Globalizations of Harish-Chandra Modules

TY - JOUR

T1 - Analytic Representation Theory of Lie Groups: General Theory and Analytic Globalizations of Harish-Chandra Modules

AU - Gimperlein, Heiko

AU - Kroetz, Bernhard

AU - Schlichtkrull, Henrik

N1 - to appear

PY - 2011/9

Y1 - 2011/9

N2 - In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra [formula omitted](G) of analytic functions of rapid decay. For reductive groups every Harish-Chandra module V is shown to admit a unique tempered analytic globalization, which is generated by V and [formula omitted](G) and which embeds as the space of analytic vectors in all Banach globalizations of V.

AB - In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra [formula omitted](G) of analytic functions of rapid decay. For reductive groups every Harish-Chandra module V is shown to admit a unique tempered analytic globalization, which is generated by V and [formula omitted](G) and which embeds as the space of analytic vectors in all Banach globalizations of V.

U2 - 10.1112/S0010437X11005392

DO - 10.1112/S0010437X11005392

M3 - Journal article

SN - 0010-437X

VL - 147

SP - 1581

EP - 1607

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 5

ER -