Speaker: Luca Cassia
Abstract: I will show how q,t-deformed matrix models give rise to representations of the deformed Virasoro algebra and more generally of the quantum toroidal gl_1 algebra (or DIM algebra). These representations are described in terms of finite difference equations, which can be reformulated as a set of recursion relations for the corralation functions. The examples considered come from localization of 3d N=2 theories, and in one case the refined Chern-Simons model. Under certain assumptions, the corresponding recursions admit unique solutions which can be phrased in terms of “superintegrability” formulas, i.e. a special form of averages of Macdonald polynomials. I will show how to use the quantum toroidal algebra relations to give a proof of several superintegrability formulas which have been previously conjectured. Finally, I will discuss relations between superintegrability and various generalizations of Macdonald interpolation polynomials. Based on work in progress with Victor Mishnyakov.
Time: 4:00 – 5:30 PM, May 22, Thursday
Location: Room 1410 at SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
Zoom Meeting ID: 838 293 7191 (Passcode: SIMIS)
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