Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized affine Springer theory and Hilbert schemes on planar curves   We show that Hilbert schemes of planar curve singularities and their
parabolic variants can be interpreted as certain generalized affine Springer
fibers for $GL_n$, as defined by Goresky-Kottwitz-MacPherson. Using a
generalization of affine Springer theory for Braverman-Finkelberg-Nakajima's
Coulomb branch algebras, we construct a rational Cherednik algebra action on
the homology of the Hilbert schemes, and compute it in examples. Along the way,
we generalize to the parahoric setting the recent construction of
Hilburn-Kamnitzer-Weekes, which may be of independent interest. In the
spherical case, we make our computations explicit through a new general
localization formula for Coulomb branches. Via results of Hogancamp-Mellit, we
also show the rational Cherednik algebra acts on the HOMFLY homologies of torus
knots. This work was inspired in part by a construction in three-dimensional
$\mathcal{N}=4$ gauge theory.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio