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Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative
4 videos

Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative

Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints
3 videos

Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints

Not Only Scalar Curvature Seminar
60 videos

Not Only Scalar Curvature Seminar

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models
4 videos

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models

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Combinatorics and Arithmetic for Physics: special days 2023

Collection Combinatorics and Arithmetic for Physics: special days 2023

Organizer(s) Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV and Karol A. PENSON
Date(s) 15/11/2023 - 17/11/2023
linked URL https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP10_2023.html
00:00:00 / 00:00:00
17 27

Quantum relativistic Toda Hamiltonians associated with a family of cluster algebras

By Rinat Kedem

The quantum relativistic Toda Hamiltonians for classical root systems are obtained as the q-Whittaker limit of (dual) Macdonald operators or specialized Koornwinder operators. They are the conserved quantities of discrete evolutions in a family of quantum cluster algebras known as Q-systems. The polynomial eigenfunctions (q-Whittaker functions) can be constructed from the action of a subset of A-type cluster variables, which act as raising operators. This gives a uniform description for all classical root systems of such eigenfuctions. In some cases, the augmented cluster algebra quiver also gives a candidate for Baxter operators commuting with the quantum Hamiltonians. Joint with Philippe Di Francesco.

Information about the video

  • Date of recording 16/11/2023
  • Date of publication 22/11/2023
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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