FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 7, PAGES 85-225

Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture

A. I. Shtern

Abstract

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In this paper, a description of the structure of all finite-dimensional, locally bounded quasirepresentations of arbitrary connected Lie groups is given and the proof of Mishchenko's conjecture for connected, locally compact groups and a proof of an analog of the van der Waerden theorem (i.e., the automatic continuity condition for all locally bounded, finite-dimensional representations) for the commutator subgroup of an arbitrary connected Lie group are presented.

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