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arXiv · 1508.03586

A multiplicative analogue of complex symplectic implosion

Andrew Dancer·Frances Kirwan
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Abstract

We introduce a multiplicative version of complex-symplectic implosion in the case of $SL(n, \C)$. The universal multiplicative implosion for $SL(n, \C)$ 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 $SL(n, \C)$. We also explain how the real symplectic group-valued universal implosion introduced by Hurtubise, Jeffrey and Sjamaar may be identified inside this space.

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Andrew Dancer, Frances Kirwan. 2015-08-14. A multiplicative analogue of complex symplectic implosion. https://arxiv.org/abs/1508.03586

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