Speaker: Paul Levy (University of Lancaster, UK).
Abstract: It is well-known that nilpotent orbits in \sl_n(\C) correspond bijectively with partitions of n, such that the closure (partial) ordering on orbits is sent to the dominance order on partitions. Taking dual partitions simply turns this partially ordered set upside down, so there is an order-reversing involution on the set of nilpotent orbits. More generally, if \g is any simple Lie algebra over \C then Lusztig-Spaltenstein duality is an order-reversing bijection from the set of special nilpotent orbits in \g to the set of special nilpotent orbits in the Langlands dual Lie algebra \g^L.
To each edge in the Hasse diagram of special nilpotent orbits is associated a symplectic singularity. It was observed by Kraft and Procesi that, for \sl_n, the duality swaps a Kleinian singularity of type A_k for the minimal nilpotent orbit closure in \sl_{k+1} (and vice-versa). This can be thought of as a version of mirror symmetry between Higgs and Coulomb branches. In this talk, I will explain how this mirror symmetry extends to the other simple Lie algebras (with some caveats). This is joint research with Juteau and Sommers.
Time: Wednesday 30th April at 4 pm
Location: online
Zoom Meeting ID: 844 0850 4400 (Passcode: 031828)
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