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Published on Jul 12, 2016
Talk of Vyacheslav Futorny "Mischenko-Fomenko subalgebras Vinberg's problem Conjecture of Feigin, Frenkel and Toledano Laredo" on Kyiv Mathematical Colloquium.
Abstract: "For a simple Lie algebra g, and any μ ∈ g* one can define a Poisson commutative subalgebra of the symmetric algebra S(g), which is called Mischenko-Fomenko subalgebra, or shift of argument subalgebra. If μ is regular then this subalgebra admits a quantization to a maximal commutative subalgebra of the universal enveloping algebra U(g) (this is known as Vinberg's problem). It was conjectured by Feigin, Frenkel and Toledano Laredo that quantization process works in non-regular case as well. Proof of this conjecture for g of type A was recently found in a joint work with Alexander Molev (Sydney, Australia). These and other recent results and their applications will be discussed."