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Quantization of nilpotent coadjoint -orbit closures in positive characteristics
Filippo Ambrosio, Lewis Topley, Matthew Westaway
Let be a reductive group over an algebraically closed field of positive characteristic , good for the root system of . The closures of -orbits in the Hilbert nullcone…
Sheets, Jordan classes and induced orbits in the exotic and enhanced modules
Filippo Ambrosio, Giovanna Carnovale, Francesco Esposito +2
Kato developed an exotic Deligne-Langlands correspondence using a geometric model for the multiparameter affine Hecke algebra of type C, based on his exotic nilpotent cone. Achar-H…
Hyperplane arrangements and Vinberg's -groups
Filippo Ambrosio, Andrea Santi
Let be a periodically graded semisimple complex Lie algebra. In this note, we give a uniform proof of the…
Étale geometry of closures of Jordan classes
Filippo Ambrosio
Let be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a…
Equivariant deformation theory for nilpotent slices in symplectic Lie algebras
Filippo Ambrosio, Lewis Topley
The Slodowy slice is a flat Poisson deformation of its nilpotent part, and it was demonstrated by Lehn-Namikawa-Sorger that there is an interesting infinite family of nilpotent orb…
A parametrization of sheets of conjugacy classes in bad characteristic
Filippo Ambrosio, Giovanna Carnovale, Francesco Esposito
Let G be a simple algebraic group of adjoint type over an algebraically closed field of bad characteristic. We show that its sheets of conjugacy classes are parametrized by G-conju…
Spherical birational sheets in reductive groups
Filippo Ambrosio, Mauro Costantini
We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when is a connected reductive complex…
Universal filtered quantizations of nilpotent Slodowy slices
Filippo Ambrosio, Giovanna Carnovale, Francesco Esposito +1
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by sh…
Birational sheets in reductive groups
Filippo Ambrosio
We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras. For G semisimple simply connected, we describe birational sheets in…
Local geometry of Jordan classes in semisimple algebraic groups
Filippo Ambrosio, Giovanna Carnovale, Francesco Esposito
We prove that the closure of every Jordan class J in a semisimple simply connected complex group G at a point x with Jordan decomposition x = rv is smoothly equivalent to the union…