Crepant Resolutions of a Slodowy Slice in a Nilpotent Orbit Closure in $\mathfrak {sl}_N(\mathbb C)$

Abstract

One of our results of this article is that every (projective) crepant resolution of a Slodowy slice in a nilpotent orbit closure in sl N (C) can be obtained as the restriction of some crepant resolution of the nilpotent orbit closure. We also show that there is a decomposition of the Slodowy slice into other Slodowy slices with good properties. From this decomposition, one can count the number of crepant resolutions.

D n Dynkin quiver moduli spaces

“…Consider two balanced quivers Q 1 bal and Q 2 bal with gauge nodes with positive rank g 1 i and g 2 i respectively 15 . Attached to these gauge nodes are non-negative flavour nodes with label f 1 i and…”

“…. of classical and exceptional Lie algebras, [7] - [15] have been the subject of numerous papers in recent years [16] - [27]. Work has often involved using 3d N = 4 quiver gauge theories as tools with which to construct the varieties which also arise as nilpotent varieties of Lie algebras.…”

“…Note that in the literature, 'D n quiver' is often used to refer to quivers that would be more properly called D n Dynkin quivers 1 , for example in [6]. The specifics of the connections between quiver gauge theories and the nilpotent cones of classical and exceptional Lie algebras, [7][8][9][10][11][12][13][14][15] have been the subject of numerous papers in recent years [16][17][18][19][20][21][22][23][24][25][26][27]. Work has often involved using 3d N = 4 quiver gauge theories as tools with which to construct the varieties which also arise as nilpotent varieties of Lie algebras.…”

“…This changes the gauge node topology since the rank zero nodes are effectively absent. This includes the possibility that Q 3 is a disjoint quiver 15. Where the lower index refers to some ordering of the gauge nodes which is maintained across quivers.…”