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2014 Yangians and quantizations of slices in the affine Grassmannian
Joel Kamnitzer, Ben Webster, Alex Weekes, Oded Yacobi
Algebra Number Theory 8(4): 857-893 (2014). DOI: 10.2140/ant.2014.8.857

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 PGLn of Finkelberg and Rybnikov.

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Joel Kamnitzer. Ben Webster. Alex Weekes. Oded Yacobi. "Yangians and quantizations of slices in the affine Grassmannian." Algebra Number Theory 8 (4) 857 - 893, 2014. https://doi.org/10.2140/ant.2014.8.857

Information

Received: 10 January 2013; Revised: 2 August 2013; Accepted: 31 August 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1325.14068
MathSciNet: MR3248988
Digital Object Identifier: 10.2140/ant.2014.8.857

Subjects:
Primary: 20G42
Secondary: 14D24, 14M15, 53D55

Rights: Copyright © 2014 Mathematical Sciences Publishers

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