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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