A moment map for a symplectic group action is a map 
whose pairing with an Lie algebra element generates that infinitesimal action
through the symplectic form. With the convention
, the
cotangent lift of a linear action on 
has
 |
where 
and the symplectic form is 
for the tautological cotangent 1-form 
. The sign convention must be matched to the symplectic
form. Quotients of a zero moment-map locus with a stability condition define
Nakajima quiver varieties.
