A remark on Mishchenko-Fomenko algebras and regular sequences
arXiv:1703.00880
Abstract
In this note, we show that the free generators of the Mishchenko-Fomenko subalgebra of a complex reductive Lie algebra, constructed by the argument shift method at a regular element, form a regular sequence. This result was proven by Serge Ovsienko in the type A at a regular and semisimple element. Our approach is very different, and is strongly based on geometric properties of the nilpotent bicone.
The proof of the main result has been shortened. To appear in Selecta Math