Room P4.35, Mathematics Building

Pavel Etingov, Massachusetts Institute of Technology
D-modules on Poisson varieties and Poisson traces.

Let \(V\) be an affine symplectic algebraic variety over \(\mathbb{C}\), and \(G\) a finite group of automorphisms of \(V\) (for example, \(V\) is a symplectic vector space, and \(G\) is a subgroup of \(\mathop{Sp}(V)\)). Let \(A\) be the algebra of regular functions on \(V/G\), and \(E\) be the space of linear functionals on \(A\) which are invariant under Hamiltonian vector fields on \(V/G\) (so called Poisson traces). It turns out that \(E\) is finite dimensional. I will explain how to prove and generalize this statement, using the theory of D-modules, and will also describe some applications to noncommutative algebra. This is joint work with Travis Schedler.