Compact homogeneous spaces of reductive Lie groups and spaces close to them

2016 ◽  
Vol 207 (3) ◽  
pp. 342-357 ◽  
Author(s):  
V V Gorbatsevich
Keyword(s):  
Lie Groups ◽  
Homogeneous Spaces ◽  
Reductive Lie Groups

scholarly journals Characteristic Cycles and Wave Front Cycles of Representations of Reductive Lie Groups

2000 ◽  
Vol 151 (3) ◽  
pp. 1071 ◽  
Author(s):  
Wilfried Schmid ◽  
Kari Vilonen
Keyword(s):  
Wave Front ◽  
Lie Groups ◽  
Reductive Lie Groups

Parabolic Higgs Bundles for Real Reductive Lie Groups

2018 ◽  
pp. 653-680 ◽  
Author(s):  
Ignasi Mundet i Riera
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Lie Group ◽  
Vector Bundles ◽  
Structure Group ◽  
Higgs Bundles ◽  
Local Systems ◽  
Parabolic Structure ◽  
Reductive Lie Groups ◽  
Reductive Lie Group

This chapter explains the correspondence between local systems on a punctured Riemann surface with the structure group being a real reductive Lie group G, and parabolic G-Higgs bundles. The chapter describes the objects involved in this correspondence, taking some time to motivate them by recalling the definitions of G-Higgs bundles without parabolic structure and of parabolic vector bundles. Finally, it explains the relevant polystability condition and the correspondence between local systems and Higgs bundles.

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