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2015 The topology of nilpotent representations in reductive groups and their maximal compact subgroups
Maxime Bergeron
Geom. Topol. 19(3): 1383-1407 (2015). DOI: 10.2140/gt.2015.19.1383

Abstract

Let G be a complex reductive linear algebraic group and let K G be a maximal compact subgroup. Given a nilpotent group Γ generated by r elements, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) with the natural topology induced from an embedding into Gr and Kr respectively. The goal of this paper is to prove that there is a strong deformation retraction of Hom(Γ,G) onto Hom(Γ,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(Γ,G)G onto the ordinary quotient Hom(Γ,K)K.

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Maxime Bergeron. "The topology of nilpotent representations in reductive groups and their maximal compact subgroups." Geom. Topol. 19 (3) 1383 - 1407, 2015. https://doi.org/10.2140/gt.2015.19.1383

Information

Received: 15 December 2013; Accepted: 25 July 2014; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1346.20063
MathSciNet: MR3352239
Digital Object Identifier: 10.2140/gt.2015.19.1383

Subjects:
Primary: 20G20
Secondary: 20G05, 55P99

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.19 • No. 3 • 2015
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