Farkhod Eshmatov
Sichuan University (Chengdu, China)
Dixmier subgroups of the affine Cremona group.
Abstract: In this talk, we will discuss a class of infinite-dimensional (ind-algebraic) groups Gn closely related to the group of polynomial automorphisms of the affine plane. These groups originate from the theory of integrable systems and can be realized geometrically as automorphism groups of rings of differential operators on singular spectral curves. By analogy with affine algebraic groups, we define the notion of a Borel subgroup and prove an infinite-dimensional version of a classical theorem of R.Steinberg characterizing these subgroups in Gn in abstract terms. Then we show that up to conjugation there are exactly p(n), where p(n) is the number of partitions of n, Borel subgroups of Gn. (Joint work with Y.Berest and F.Eshmatov)