#### Vol. 8, No. 4, 2014

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Yangians and quantizations of slices in the affine Grassmannian

### Joel Kamnitzer, Ben Webster, Alex Weekes and Oded Yacobi

Vol. 8 (2014), No. 4, 857–893
##### Abstract

We study quantizations of transverse slices to Schubert varieties in the affine Grassmannian. The quantization is constructed using quantum groups called shifted Yangians — these are subalgebras of the Yangian we introduce which generalize the Brundan–Kleshchev shifted Yangian to arbitrary type. Building on ideas of Gerasimov, Kharchev, Lebedev and Oblezin, we prove that a quotient of the shifted Yangian quantizes a scheme supported on the transverse slices, and we formulate a conjectural description of the defining ideal of these slices which implies that the scheme is reduced. This conjecture also implies the conjectural quantization of the Zastava spaces for PGL${}_{n}$ of Finkelberg and Rybnikov.

##### Keywords
quantization, affine Grassmannian, quantum groups, Yangian
##### Mathematical Subject Classification 2010
Primary: 20G42
Secondary: 53D55, 14M15, 14D24