A multiplicative analogue of complex symplectic implosion

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• 作者：Andrew Dancer ; Frances Kirwan
• 关键词：Implosion ; Hyperk?hler ; Nonreductive quotient ; 53C26 ; 53D20 ; 14L24
• 刊名：European Journal of Mathematics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：1
• 期：4
• 页码：655-668
• 全文大小：432 KB
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• 作者单位：Andrew Dancer (1)
  Frances Kirwan (2)
  
  1. Jesus College, Turl St., Oxford, OX1 3DW, UK
  2. Balliol College, Broad St., Oxford, OX1 3BJ, UK
  
• 刊物类别：Algebraic Geometry;
• 刊物主题：Algebraic Geometry;
• 出版者：Springer International Publishing
• ISSN：2199-6768

文摘

We introduce a multiplicative version of complex-symplectic implosion in the case of \(\mathrm{SL}(n, {\mathbb C})\). The universal multiplicative implosion for \(\mathrm{SL}(n, {\mathbb C})\) is an affine variety and can be viewed as a nonreductive geometric invariant theory quotient. It carries a torus action and reductions by this action give the Steinberg fibres of \(\mathrm{SL}(n, {\mathbb C})\). We also explain how the real symplectic group-valued universal implosion introduced by Hurtubise, Jeffrey and Sjamaar may be identified inside this space. Keywords Implosion Hyperk?hler Nonreductive quotient