Fukaya–Seidel categories of Hilbert schemes and parabolic category O
Fukaya–Seidel categories of Hilbert schemes and parabolic category O
We realise Stroppel’s extended arc algebra [13, 51] in the Fukaya–Seidel category of a natural Lefschetz fibration on the generic fibre of the adjoint quotient map on a type A nilpotent slice with two Jordan blocks, and hence obtain a symplectic interpretation of certain parabolic two-block versions of Bernstein–Gel’fand–Gel’fand category O. As an application, we give a new geometric construction of the spectral sequence from annular to ordinary Khovanov homology. The heart of the paper is the development of a cylindrical model to compute Fukaya categories of (affine open subsets of) Hilbert schemes of quasi-projective surfaces, which may be of independent interest.
Fukaya Seidel category, nilpotent slices, Hilbert scheme, Arc algebra, Khovanov homology, BGG category O
3215–3332
Mak, Cheuk Yu
49c234b8-842f-4cda-b082-d36505c24626
Smith, Ivan
aca49063-44b7-4fde-8a3f-5cad9279cca6
Mak, Cheuk Yu
49c234b8-842f-4cda-b082-d36505c24626
Smith, Ivan
aca49063-44b7-4fde-8a3f-5cad9279cca6
Mak, Cheuk Yu and Smith, Ivan
(2021)
Fukaya–Seidel categories of Hilbert schemes and parabolic category O.
Journal of the European Mathematical Society, 9, .
(doi:10.4171/JEMS/1159).
Abstract
We realise Stroppel’s extended arc algebra [13, 51] in the Fukaya–Seidel category of a natural Lefschetz fibration on the generic fibre of the adjoint quotient map on a type A nilpotent slice with two Jordan blocks, and hence obtain a symplectic interpretation of certain parabolic two-block versions of Bernstein–Gel’fand–Gel’fand category O. As an application, we give a new geometric construction of the spectral sequence from annular to ordinary Khovanov homology. The heart of the paper is the development of a cylindrical model to compute Fukaya categories of (affine open subsets of) Hilbert schemes of quasi-projective surfaces, which may be of independent interest.
Text
FScyl_6th_JEMS_Aug22_2021
- Accepted Manuscript
Text
3108902-10.4171-jems-1159-print
- Version of Record
More information
Accepted/In Press date: 20 October 2021
e-pub ahead of print date: 20 October 2021
Keywords:
Fukaya Seidel category, nilpotent slices, Hilbert scheme, Arc algebra, Khovanov homology, BGG category O
Identifiers
Local EPrints ID: 477070
URI: http://eprints.soton.ac.uk/id/eprint/477070
ISSN: 1435-9855
PURE UUID: d15ad4dd-7c97-433e-90f7-a585bce82ed5
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Date deposited: 25 May 2023 16:44
Last modified: 17 Mar 2024 04:17
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Author:
Cheuk Yu Mak
Author:
Ivan Smith
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