Special Colloquium/Candidate Presentation: Non-stationary difference equation for q-Virasoro algebra
- Event Type
- Seminar/Symposium
- Sponsor
- n/a
- Virtual
- Join online
- Date
- Jan 18, 2022 2:00 pm
- Speaker
- Shamil Shakirov (University of Geneva)
- Contact
- Rinat Kedem
- rinat@illinois.edu
- Views
- 76
Abstract: 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.