Non-stationary difference equation for q-Virasoro conformal blocks
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914218039574528 |
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| author | Shakirov, Shamil |
| author_facet | Shakirov, Shamil |
| contents | Conformal blocks of q,t-deformed Virasoro and W-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov-Shatashvili limit t -> 1, whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic t <> 1 is a non-stationary Schrodinger equation where t parametrizes shift in time. In this paper we make the non-stationary equation explicit for the q,t-Virasoro block with one degenerate and four generic Verma modules, and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_07939 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-stationary difference equation for q-Virasoro conformal blocks Shakirov, Shamil Representation Theory High Energy Physics - Theory Mathematical Physics Quantum Algebra Conformal blocks of q,t-deformed Virasoro and W-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov-Shatashvili limit t -> 1, whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic t <> 1 is a non-stationary Schrodinger equation where t parametrizes shift in time. In this paper we make the non-stationary equation explicit for the q,t-Virasoro block with one degenerate and four generic Verma modules, and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials. |
| title | Non-stationary difference equation for q-Virasoro conformal blocks |
| topic | Representation Theory High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2111.07939 |