University of Birmingham > Talks@bham > Algebra Seminar > Dual singularities in exceptional type nilpotent cones

## Dual singularities in exceptional type nilpotent conesAdd to your list(s) Download to your calendar using vCal - Paul Levy, University of Lancaster
- Thursday 06 November 2014, 16:00-17:00
- Physics West 117.
If you have a question about this talk, please contact David Craven. It is well-known that nilpotent orbits in sl C then Lusztig-Spaltenstein duality is an order-reversing bijection from the set of special nilpotent orbits in to the set of special nilpotent orbits in the Langlands dual Lie algebra gg^{L}. It was observed by Kraft and Procesi that the duality in type A is manifested in the geometry of the nullcone. In particular, if two orbits O_{1}<O_{2} are adjacent in the partial order then so are their duals O_{1}^{t}>O_{2}^{t}, and the isolated singularity attached to the pair (O_{1}, O_{2}) is dual to the singularity attached to (O_{2}^{t},O_{1}^{t}): a Kleinian singularity of type A_{k} is swapped with the minimal nilpotent orbit closure in sl_{k+1} (and vice-versa). Subsequent work of Kraft-Procesi determined singularities associated to such pairs in the remaining classical Lie algebras, but did not specifically touch on duality for pairs of special orbits. In this talk, I will explain some recent joint research with Fu, Juteau and Sommers on singularities associated to pairs O_{1} 2 of (special) orbits in exceptional Lie algebras. In particular, we (almost always) observe a generalized form of duality for such singularities in any simple Lie algebra.This talk is part of the Algebra Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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