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(minicours) D. Volin: Young tableaux and quantum integrability
Dmytro Volin will give 5 mini-courses about « Young tableaux and quantum integrability », with the following a priori schedule:
Lecture 1 (march 26): Multiplication of Young tableaux through “Jeu de taquin”. Plactic monoid.
Lecture 2 (march 28): Knuth-Robinson-Schensted correspondence. Algebra of symmetric functions.
Lecture 3 (march 29): Schur-Weyl duality and related topics of representation theory of GL(N) and S_L
Lecture 4 (april 2): Selected combinatorial questions in quantum integrability. Rigged configurations and crystal bases.
Lecture 5 (april 4): Supertableaux. Super-symmetric functions. Non-compact Young diagrams and applications to representation theory of su(p,q|m) and AdS/CFT integrability.
Some parts of lectures will be designed as problem-solving sessions. Depending on the audience progress through these sessions and feedback, the speed and depth at which material is presented can be altered.
Literature: Lectures 1-3 will closely follow parts 1,2 of the book “Young tableaux” by W.Fulton. Lecture 4 aims to summarise results of a handful of research papers, most of them are cited in the introduction of 1607.03232. Lecture 5 aims to present results of 1712.01811 and 1701.03704.