2012/05/31 by Carla Farsi, Hans-Christian Herbig, Christopher Seaton · 1 citation
Mathematics · #math.SG #math.RT #msc:53D20 #msc:58A40 #msc:13A50 #msc:14L24 #msc:57R18
paper · pdf · doi:10.3842/sigma.2013.032
published as SIGMA 9 (2013), 032, 33 pages
arxiv created 2013/04/12 · arxiv updated 2013/04/15
We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic representation of a finite group, while the corresponding GIT quotients are smooth. Additionally, we relate the question of simplicialness of a torus representation to Gaussian elimination.