Семинар НУЛ АГП "The Popov-Pommerening conjecture for groups of small rank"

Let G be a reductive group over an algebraically closed field K of characteristic zero, and let H be a subgroup of G normalized by a maximal torus. The Popov–Pommerening conjecture asserts that, for any affine G-variety X, the algebra of invariants K[X]^H is finitely generated. In fact, this reduces to the question of whether the algebra K[G]^H is finitely generated. This conjecture has been proved in some special cases. We will discuss a new approach to checking the conjecture, which leads to an explicit algorithm for constructing generators of the algebra K[G]^H. We use it to prove the conjecture for groups G of small rank, including all cases with rank ≤ 3.