Landau–Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety
| dc.contributor.author | Tarasov, Vitaly | |
| dc.contributor.author | Varchenko, Alexander | |
| dc.contributor.department | Mathematical Sciences, School of Science | |
| dc.date.accessioned | 2024-01-23T18:53:32Z | |
| dc.date.available | 2024-01-23T18:53:32Z | |
| dc.date.issued | 2023-02 | |
| dc.description.abstract | We consider the system of quantum differential equations for a partial flag variety and construct a basis of solutions in the form of multidimensional hypergeometric functions, that is, we construct a Landau–Ginzburg mirror for that partial flag variety. In our construction, the solutions are labeled by elements of the K-theory algebra of the partial flag variety. To establish these facts we consider the equivariant quantum differential equations for a partial flag variety and introduce a compatible system of difference equations, which we call the qKZ equations. We construct a basis of solutions of the joint system of the equivariant quantum differential equations and qKZ difference equations in the form of multidimensional hypergeometric functions. Then the facts about the non-equivariant quantum differential equations are obtained from the facts about the equivariant quantum differential equations by a suitable limit. Analyzing these constructions we obtain a formula for the fundamental Levelt solution of the quantum differential equations for a partial flag variety. | |
| dc.eprint.version | Final published version | |
| dc.identifier.citation | Tarasov, V., & Varchenko, A. (2023). Landau–Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety. Journal of Geometry and Physics, 184, 104711. https://doi.org/10.1016/j.geomphys.2022.104711 | |
| dc.identifier.uri | https://hdl.handle.net/1805/38120 | |
| dc.language.iso | en_US | |
| dc.publisher | Elsevier | |
| dc.relation.isversionof | 10.1016/j.geomphys.2022.104711 | |
| dc.relation.journal | Journal of Geometry and Physics | |
| dc.rights | Attribution 4.0 International | en |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0 | |
| dc.source | ArXiv | |
| dc.subject | dynamical differential equations | |
| dc.subject | qKZ difference equations | |
| dc.subject | quantum differential equations | |
| dc.subject | q- hypergeometric solutions | |
| dc.title | Landau–Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety | |
| dc.type | Article |