Quantum Argument–Shift Subalgebras via Quantized Shift Operators

Running Seminar
The argument–shift method constructs maximal Poisson-commutative subalgebras of the symmetric algebra $S(mathfrak g)$ of a Lie algebra $mathfrak g$ with respect to the Lie–Poisson bracket. Their quantizations—known as quantum argument–shift subalgebras—form maximal commutative subalgebras of the universal enveloping algebra $U(mathfrak g)$ and play a fundamental role in quantum integrable systems. Although existence and uniqueness of these quantizations have been established in many cases, the underlying argument–shift procedures, realized as derivations of $S(mathfrak g)$, had not previously been quantized. Recently, Yasushi Ikeda and I defined quantized argument–shift procedures for $mathfrak{gl}_n$ and proved that they generate the associated quantum argument–shift subalgebras.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.