2012/09/30 by Joel Kamnitzer, Ben Webster, Alex Weekes +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Algorithm #Conjecture #Grassmannian #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum mechanics #Quotient #Scheme (mathematics) #Yangian #math.AG #math.QA #math.RA
paper · pdf · doi:10.2140/ant.2014.8.857
published as Algebra Number Theory 8 (2014), no. 4, 857-893 · 37 pages; v2, slightly strengthened Theorem 2.9
arxiv created 2013/02/21 · openalex publication_date 2014/08/10 · arxiv updated 2014/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.