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Special Colloquium/Candidate Presentation: Non-stationary difference equation for q-Virasoro algebra

Event Type
Seminar/Symposium
Sponsor
n/a
Virtual
wifi event
Date
Jan 18, 2022   2:00 pm  
Speaker
Shamil Shakirov (University of Geneva)
Contact
Rinat Kedem
E-Mail
rinat@illinois.edu
Views
66

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. 

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