Kleinian singularities: some geometry, combinatorics and representation theory
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916449578123264 |
|---|---|
| author | Bertsch, Lukas Gyenge, Ádám Szendrői, Balázs |
| author_facet | Bertsch, Lukas Gyenge, Ádám Szendrői, Balázs |
| contents | We review the relationship between discrete groups of symmetries of Euclidean three-space, constructions in algebraic geometry around Kleinian singularities including versions of Hilbert and Quot schemes, and their relationship to finite-dimensional and affine Lie algebras via the McKay correspondence. We focus on combinatorial aspects, such as the enumeration of certain types of partition-like objects, reviewing in particular a recently developed root-of-unity-substitution calculus. While the most complete results are in type A, we also develop aspects of the theory in type D, and end with some questions about the exceptional type E cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kleinian singularities: some geometry, combinatorics and representation theory Bertsch, Lukas Gyenge, Ádám Szendrői, Balázs Algebraic Geometry Combinatorics We review the relationship between discrete groups of symmetries of Euclidean three-space, constructions in algebraic geometry around Kleinian singularities including versions of Hilbert and Quot schemes, and their relationship to finite-dimensional and affine Lie algebras via the McKay correspondence. We focus on combinatorial aspects, such as the enumeration of certain types of partition-like objects, reviewing in particular a recently developed root-of-unity-substitution calculus. While the most complete results are in type A, we also develop aspects of the theory in type D, and end with some questions about the exceptional type E cases. |
| title | Kleinian singularities: some geometry, combinatorics and representation theory |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2410.17860 |