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Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
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Matrix models: superintegrability and W-representation V. V. Mishnyakovabcd a Institute for Theoretical and Mathematical Physics of Lomonosov Moscow State University b P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region d Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre «Kurchatov Institute» |
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Abstract: I will discuss some recent progress in understanding the relationships between several phenomena in the field of matrix models. On the one hand, the question of the relationship between superintegrability, Virasoro conditions and standard integrability in the sense of the Toda equations will be considered, using the Gaussian matrix model as an example. An attempt to derive superintegrability from the Virasoro conditions leads to the construction of W-representations for matrix models and the study of the action of W-operators on Schur functions and their deformations. As two applications, we will consider the proof of superintegrability for the Gaussian β-deformed matrix model, and the construction of a non-Abelian W-representation for the generalized Kontsevich model. |
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