University of Birmingham > Talks@bham > Birmingham Algebra Seminar  >  The quaternionic x dihedral group of order 32 quotient singularity is also a quiver variety, as are its 81 crepant resolutions.

The quaternionic x dihedral group of order 32 quotient singularity is also a quiver variety, as are its 81 crepant resolutions.

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  • UserTravis Schedler (Imperial College London)
  • ClockWednesday 02 February 2022, 15:30-16:30
  • HouseZoom.

If you have a question about this talk, please contact Gareth Tracey.

I will consider the order-32 central product of the 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 Nakajima quiver variety. We will prove this, using basic representation theory and geometry. This allows us to give a new description of all 81 crepant resolutions of the singularity, which are all given as hyperpentagon spaces (a hyperkaehler version of the moduli of pentagons in R3). Moving beyond this, we prove that all crepant resolutions of the analogous quiver cone for the n-pointed star are also hyperpolygon spaces. For example, there are precisely 1684 hyperhexagon spaces. The count uses the combinatorics of hyperplane arrangements.

This talk is part of the Birmingham Algebra Seminar series.

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