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CATEGORIES:Algebra seminar
SUMMARY: The quaternionic x dihedral group of order 32 quo
tient singularity is also a quiver variety\, as ar
e its 81 crepant resolutions. - Travis Schedler (I
mperial College London)
DTSTART:20220202T153000Z
DTEND:20220202T163000Z
UID:TALK4752AT
URL:/talk/index/4752
DESCRIPTION:I will consider the order-32 central product of th
e quaternionic and dihedral groups of order eight\
, which naturally acts via symplectic four-by-four
matrices. The quotient is a fascinating singular
cone which was predicted in 2015 by physicists to
be isomorphic to a quite different object\, a Nak
ajima quiver variety. We will prove this\, using
basic representation theory and geometry. This all
ows us to give a new description of all 81 crepant
resolutions of the singularity\, which are all gi
ven as hyperpentagon spaces (a hyperkaehler versio
n of the moduli of pentagons in R3). Moving beyon
d this\, we prove that all crepant resolutions of
the analogous quiver cone for the n-pointed star a
re also hyperpolygon spaces. For example\, there a
re precisely 1684 hyperhexagon spaces. The count u
ses the combinatorics of hyperplane arrangements.
LOCATION:Zoom
CONTACT:Gareth Tracey
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