Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.20270 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916922770063360 |
|---|---|
| author | Belkale, Prakash Mukhin, Evgeny Varchenko, Alexander |
| author_facet | Belkale, Prakash Mukhin, Evgeny Varchenko, Alexander |
| contents | The $\frak{sl}_2$ KZ differential equations with values in the tensor power of the fundamental representation with parameter $κ=\pm 2$ are considered. A Satake-type correspondence is established over complex numbers and subsequently reduced to finite characteristic. This correspondence enables the study of the KZ equations on the lower weight subspaces of the tensor power in terms of the wedge powers of the weight subspace of the weight just below the highest weight.
We apply this approach to analyze the $p$-curvature operators associated with our KZ equations, evaluate the dimension of the solution space in characteristic $p$, and determine whether all solutions are generated by the so-called $p$-hypergeometric solutions. In particular, we show that not all solutions of the KZ equations with $κ=2$ in characteristic $p$ are generated by $p$-hypergeometric solutions. Previously, no such examples were known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p$-curvature operators and Satake-type phenomenon for $\frak{sl}_2$ KZ equations with $κ=\pm 2$ Belkale, Prakash Mukhin, Evgeny Varchenko, Alexander Number Theory Exactly Solvable and Integrable Systems The $\frak{sl}_2$ KZ differential equations with values in the tensor power of the fundamental representation with parameter $κ=\pm 2$ are considered. A Satake-type correspondence is established over complex numbers and subsequently reduced to finite characteristic. This correspondence enables the study of the KZ equations on the lower weight subspaces of the tensor power in terms of the wedge powers of the weight subspace of the weight just below the highest weight. We apply this approach to analyze the $p$-curvature operators associated with our KZ equations, evaluate the dimension of the solution space in characteristic $p$, and determine whether all solutions are generated by the so-called $p$-hypergeometric solutions. In particular, we show that not all solutions of the KZ equations with $κ=2$ in characteristic $p$ are generated by $p$-hypergeometric solutions. Previously, no such examples were known. |
| title | $p$-curvature operators and Satake-type phenomenon for $\frak{sl}_2$ KZ equations with $κ=\pm 2$ |
| topic | Number Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2508.20270 |