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Explore advanced mathematical research in this lecture examining the connection between Macdonald functions and quantum dilogarithms in type A theory. Delve into the extension of q-Whittaker function theory beyond classical types, building upon the established quantum cluster algebra realization framework. Learn about newly proposed Givental-like and Mellin-Barnes-like expressions for Macdonald functions and investigate their mathematical properties through extensive application of quantum dilogarithms. Examine ongoing collaborative research findings that bridge quantum cluster algebras with Macdonald theory, providing insights into this sophisticated area of mathematical physics and representation theory.
