A new class of examples of group-valued moment maps

TL;DR

This paper constructs new examples of group-valued moment maps using quasi-symplectic implosion, revealing singular strata with smooth closures as quasi-Hamiltonian spaces, expanding the understanding of such geometric structures.

Contribution

It introduces new classes of group-valued moment maps by analyzing singular strata of the universal imploded space with smooth closures.

Findings

Identified singular strata with smooth closures in the universal imploded space.

Demonstrated these closures are quasi-Hamiltonian spaces.

Extended the class of known examples of group-valued moment maps.

Abstract

The purpose of this paper is to construct new examples of group-valued moment maps. As the main tool for construction of such examples we use quasi-symplectic implosion which was introduced in [HJS06]. More precisely we show that there are certain strata of $D{\bf Sp}(n)_{\rm impl}$, the universal imploded space, where it is singular but whose closure is a smooth quasi-Hamiltonian ${\bf Sp}(n) \times T$ space.