Seminario del grupo de teoría de Lie

Giovanna Carnovale – Lunes 8 de junio 14:00hs

Equivariant filtered quantisations of nilpotent Slodowy slices

Resumen:

The talk is based on joint work with F. Ambrosio, F. Esposito and L.
Topley.

After introducing the setup and recalling the crucial results of Losev and
Namikawa on the existence of a universal Poisson deformation and of a
universal filtered quantization for every conical symplectic singularity
$X$, we will show how one can construct universal $\Gamma$-deformations and universal $\Gamma$-quantizations for any group $\Gamma$ of graded Poisson automorphisms of $X$.

When $X$ is a nilpotent Slodowy slice, work of Lehn, Namikawa and Sorger
allows to verify when the corresponding finite W-algebra is the universal
filtered quantization of $X$. This is never the case if  $X$ is subregular
in a non-simply-laced Lie algebra ${\mathfrak g}_0$. Under some assumptions on the Dynkin type we will show that in this situation the
corresponding finite W-algebra is the $\Gamma$-universal quantization of
the slice: here $\Gamma$ is an automorphism group induced from the group of Dynkin automorphisms realising the root system of ${\mathfrak g}_0$ as a folding of a non-simply-laced one.
As a byproduct we will obtain a surjective filtered algebra morphism from
each subregular finite $W$-algebra for a simply-laced Lie algebra to its
«folded counterpart».
Time permitting, this result will be applied to the pair of root systems
$(A_{2n-1},B_n)$ in order to  provide a presentation of the subregular
finite W-algebra as a quotient of a shifted Yangian.