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Representations of quantized Gieseker varieties with minimal support

Algebraic Geometry

Speaker: Jose Simental Rodriguez, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~josesr/
Location: 2112 MSB
Start time: Wed, Jan 15 2020, 12:10PM

Gieseker varieties arise as the Hamiltonian reduction of the space of framed representations of the Jordan quiver. Examples of these include closures of minimal nilpotent orbits in $\mathfrak{sl}_r$, as well as symmetric products of copies of $\mathbb{C}^2$.

Quantizations of Gieseker varieties may be defined via quantum Hamiltonian reduction, and they have an interesting representation theory. I will explain how to construct their representations using equivariant D-modules on $\mathfrak{sl}_r$ and how to study some of these representations by introducing an auxiliary algebra that is similar to the type A rational Cherednik algebra. This allows us to obtain character formulas for these representations. In particular, we obtain dimension and character formulas for finite-dimensional representations, as well as a combinatorial interpretation of these. This is based on joint work with Pavel Etingof, Vasily Krylov and Ivan Losev.