Algebra and Geometry Seminar
Quantized Gieseker algebras arise as the quantum Hamiltonian reduction of the algebra of differential operators on the framed representation space of the Jordan quiver. Examples of these include algebras of differential operators on projective space as well as type A spherical rational Cherednik algebras. It turns out that when a quantized Gieseker algebra admits a finite-dimensional representation, the category of its finite-dimensional representations is equivalent to that of vector spaces. I will give all necessary definitions and then explain how the unique irreducible finite-dimensional representation of the quantized Gieseker algebra can be obtained from the finite-dimensional representation of the type A (full) rational Cherednik algebra, which allows us to compute the dimension (and character) of this representation. This is joint work with P. Etingof, V. Krylov and I. Losev.