Manifolds, Vector Bundles, and Lie Groups

1996 ◽  
pp. 529-557
Author(s):  
Michael E. Taylor
Keyword(s):  
Lie Groups ◽  
Vector Bundles

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.

scholarly journals Poisson transforms and mixed automorphic forms on semisimple Lie groups

2000 ◽  
Vol 61 (3) ◽  
pp. 353-370
Author(s):  
Min Ho Lee ◽  
Hyo Chul Myung
Keyword(s):  
Lie Groups ◽  
Vector Bundles ◽  
Automorphic Forms ◽  
Abelian Varieties ◽  
Semisimple Lie Groups

We discuss Poisson transforms which carry sections of certain vector bundles to mixed automorphic forms, and identify vector bundles whose sections are liftings of holomorphic forms on families of Abelian varieties via Poisson transforms.

scholarly journals Vector bundles over classifying spaces of compact Lie groups

1996 ◽  
Vol 176 (1) ◽  
pp. 109-143 ◽  
Author(s):  
Stefan Jackowski ◽  
Bob Oliver
Keyword(s):  
Lie Groups ◽  
Vector Bundles ◽  
Classifying Spaces ◽  
Compact Lie Groups

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

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