Moduli Space of Flat Sp(n)-Connections

• Main Authors: Liu, Kang-Gang, 劉康港
• Other Authors: Ho, Nan-Kuo
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/evfkws

碩士 === 國立清華大學 === 數學系所 === 105 === This thesis consists of two parts. In the first part, we recall the classical result on the relation between the moduli space of flat connections over a principal U (n)-bundle and the moduli space of flat connections over a vector bundle. In particular, there is an one-to-one correspondence when the vector bundle has a Hermitian structure h and the flat connections on it are compatible with h. In the second part, we try to find the precise condition when the structure group of the principal bundle is Sp(n), the (compact) symplectic group. To accomplish that, we need to deal with the question: What kind of complex vector bundle E can correspond to a principal S p (n)-bundle? Roughly speaking, the vector bundle need to be Hermitian and “symplectic”. As for the connection level, a flat Sp(n)-connection can correspond to the connection which is h-compatible and satisfies some relation with the symplectic structure.