期刊
ALGEBRA & NUMBER THEORY
卷 8, 期 4, 页码 857-893出版社
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/ant.2014.8.857
关键词
quantization; affine Grassmannian; quantum groups; Yangian
类别
资金
- NSF [DMS-1151473]
- NSA [H98230-10-1-0199]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1419500] Funding Source: National Science Foundation
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.
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