Philippe Di Francesco - Macdonald Functions and quantum Dilogarithm @IhesFr

Uploaded November 2025 | Updated September 2026, 2 weeks ago

The theory of $q$-Whittaker functions for classical types is known to have a (quantum) cluster algebra realization.
In this framework, a natural connection with the quantum dilogarithm is known. We show how this extends to the more general case of Macdonald theory in type A. We propose new Givental-like and Mellin-Barnes-like expressions for the Macdonald functions, and explore their properties. These involve heavy use of quantum dilogarithms.
(ongoing collaboration with M. Bershtein, J.-E. Bourgine, R. Kedem, V. Pasquier and J. Shiraishi).

Philippe Di Francesco (IPhT Saclay)

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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.

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Philippe Di Francesco - Macdonald Functions and quantum Dilogarithm

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