Yangians and quantizations of slices in the affine Grassmannian
By Joel Kamnitzer, Ben Webster, Alex Weekes, Oded Yacobi. 2012
108 citations recorded by the source corpus.
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-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-Rybnykov.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/26c027a1e5e68625f7221b9c6a47e0d3309ae038
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In Algebra and Number Theory
In Geometry and Topology
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- F. Benini
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- E. Witten
- Shlomo S. Razamat
In Mathematical Physics
Citations in the corpus
- The Coulomb Branch of 3d N = 4 Theories (2015, methodology): “The more general shifted Yangians that arise in the case of generic good quivers were introduced in [73].”