Nahms Equations and Nilpotent Orbits

by Christoff Krüger
Doctoral thesis
Date of Examination:2022-04-20
Date of issue:2022-05-31
Advisor:Prof. Dr. Viktor Pidstrygach
Referee:Prof. Dr. Viktor Pidstrygach
Referee:Prof. Dr. Thomas Schick
Persistent Address: http://dx.doi.org/10.53846/goediss-9271

 

 

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Abstract

English

P. Kronheimer has identified certain space of solutions to Nahms equations with a coadjoint orbit of a nilpotent element in a complex, semi-simple Lie algebra and that way equipped the orbit with an hyperkähler structure plus additional symmetries. In order to use nilpotent orbits as target manifolds for the theorey of generalised Seiberg-Witten equations we have to establish this identifications with solutions more explicitly. In this thesis we use a recurrence relation described by E. Cattani, A. Kaplan and W. Schmid to formulate critical steps towards the computation of explicit solutions.
Keywords: Nilpotent Orbits; Nahm's Equations
 
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