Perverse schobers of Coxeter type $\mathbb{A}$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917982609866752 |
|---|---|
| author | Dyckerhoff, Tobias Wedrich, Paul |
| author_facet | Dyckerhoff, Tobias Wedrich, Paul |
| contents | We define the concept of an $\mathbb{A}_n$-schober as a categorification of classification data for perverse sheaves on $\mathrm{Sym}^{n+1}(\mathbb{C})$ due to Kapranov-Schechtman. We show that any $\mathbb{A}_n$-schober gives rise to a categorical action of the Artin braid group $\mathrm{Br}_{n+1}$ and demonstrate how this recovers familiar examples of such actions arising from Seidel-Thomas $\mathbb{A}_n$-configurations of spherical objects in categorical Picard-Lefschetz theory and Rickard complexes in link homology theory. As a key example, we use singular Soergel bimodules to construct a factorizing family of $\mathbb{A}_n$-schobers which we refer to as Soergel schobers. We expect such families to give rise to a categorical analog of a graded bialgebra valued in a suitably defined freely generated braided monoidal $(\infty,2)$-category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perverse schobers of Coxeter type $\mathbb{A}$ Dyckerhoff, Tobias Wedrich, Paul Quantum Algebra Category Theory We define the concept of an $\mathbb{A}_n$-schober as a categorification of classification data for perverse sheaves on $\mathrm{Sym}^{n+1}(\mathbb{C})$ due to Kapranov-Schechtman. We show that any $\mathbb{A}_n$-schober gives rise to a categorical action of the Artin braid group $\mathrm{Br}_{n+1}$ and demonstrate how this recovers familiar examples of such actions arising from Seidel-Thomas $\mathbb{A}_n$-configurations of spherical objects in categorical Picard-Lefschetz theory and Rickard complexes in link homology theory. As a key example, we use singular Soergel bimodules to construct a factorizing family of $\mathbb{A}_n$-schobers which we refer to as Soergel schobers. We expect such families to give rise to a categorical analog of a graded bialgebra valued in a suitably defined freely generated braided monoidal $(\infty,2)$-category. |
| title | Perverse schobers of Coxeter type $\mathbb{A}$ |
| topic | Quantum Algebra Category Theory |
| url | https://arxiv.org/abs/2504.08496 |