On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products

DOI10.1112/BLMS.12254arXiv1806.07519MaRDI QIDQ6303259

Author name not available (Why is that?)

Publication date: 19 June 2018

Abstract: Truncated shifted Yangians are a family of algebras which naturally quantize slices in the affine Grassmannian. These algebras depend on a choice of two weights $lambda$ and $mu$ for a Lie algebra $mathfrakg$, which we will assume is simply-laced. In this paper, we relate the category $mathcalO$ over truncated shifted Yangians to categorified tensor products: for a generic integral choice of parameters, category $mathcalO$ is equivalent to a weight space in the categorification of a tensor product of fundamental representations defined by the third author using KLRW algebras. We also give a precise description of category $mathcalO$ for arbitrary parameters using a new algebra which we call the parity KLRW algebra. In particular, we confirm the conjecture of the authors that the highest weights of category $mathcalO$ are in canonical bijection with a product monomial crystal depending on the choice of parameters. This work also has interesting applications to classical representation theory. In particular, it allows us to give a classification of simple Gelfand-Tsetlin modules of $U(mathfrak{gl}_n)$ and its associated W-algebras.

This page was built for publication: On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6303259)