A multiplicative analogue of complex symplectic implosion

We introduce a multiplicative version of complex-symplectic implosion in the case of SL(n,C)SL(n,C) . The universal multiplicative implosion for SL(n,C)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)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.