Stratified hyperkahler spaces from semisimple Lie algebras

Abstract

We study singular hyperkahler quotients of the cotangent bundle of a complex semisimple Lie group as stratified spaces whose strata are hyperkahler. We focus on one particular case where the stratification satisfies the frontier condition and the partial order on the set of strata can be described explicitly by Lie theoretic data.

23 pages. v2: Section 4.2 was amended to fix an issue about properness of the Kähler potential. The one used in v1 was in fact not proper, but we replaced it in v2 by one which is proper (inducing the same Kähler structure), and the proof only requires minor changes in Lemma 4.5 (the issue was that M=0). Proposition 4.6 stays true, and no other section is affected

References in corpus (1)

• A hyperkahler structure on the cotangent bundle of a complex Lie group

Cited by in corpus (3)

• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
• Kempf-Ness type theorems and Nahm equations
• $\mathrm{Sp}(1)$-symmetric hyperkähler quantisation