literature
Literature
Authors
Jobs
Seminars
Conferences
DataBETA

Noncommutative counterparts of the Springer resolution

Apr, 2006
23 pages
e-Print:
View in:
pdf
reference search10 citations

Citations per year

20062010201420182022210
Abstract: (arXiv)
Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as the (local) geometric Langlands duality and modular representation theory. It is also related to some algebro-geometric problems, such as the derived equivalence conjecture and description of T. Bridgeland's space of stability conditions. The structure can be described as a noncommutative counterpart of the resolution, or as a tt-structure on the derived category of the resolution. The intriguing fact that the same tt-structure appears in these seemingly disparate subjects has strong technical consequences for modular representation theory.
  • [1]
    Spherical functors and braid group actions, in preparation
    • R. Anno
    • [2]
      of quantum groups at a pth root of unity and of semisimple groups in characteristic p: independence of p, Astérisque 220 (1994), 321 pp
      • H.H. Andersen
        ,
      • J.C. Jantzen
        ,
      • W. Soergel Representations
      • [3]
        R. Bezrukavnikov S Perverse sheaves on affine flags and Langlands dual group, electronic preprint Math. J, to appear in Israel
        • S. Arkhipov
      • [4]
        Groups, the loop Grassmannian, and the resolution
        • S. Arkhipov
          ,
        • R. Bezrukavnikov
          ,
        • V. Ginzburg Quantum
          • J.Am.Math.Soc. 17 (2004) 595
      • [5]
        C. R. Acad, Localisation de g-modules, (French) Sér. I. Sci. Paris Math. 292 (1981), no. 1, 15-18
        • A. Beilinson
          ,
        • J. Bernstein
        • [6]
          A generalization of Casselman’s submodule theorem, Representation theory of reductive groups (Park City, Utah, 1982), 35-52, Progr. Math., 40, Birkhäuser Boston, Boston, MA, 1983
          • A. Beilinson
            ,
          • A. Bernstein
          • [7]
            Faisceaux pervers, 5-171, Astérisque, 100, Soc. Math. France, Paris, 1982
            • A. Beilinson
              ,
            • J. Bernstein
              ,
            • P. Deligne
            • [8]
              Quantization of Hitchin’s Integrable System and Hecke Eigensheaves, preprint available at
              • A. Beilinson
                ,
              • V. Drinfeld
            • [9]
              Koszul duality patterns in representation theory
              • A. Beilinson
                ,
              • V. Ginzburg
                ,
              • W. Soergel
                • J.Am.Math.Soc. 9 (1996) 473
            • [10]

            • [11]
              M. van den Bergh, Noncommutative crepant resolutions, The legacy of Niels Henrik Abel, 749-770 Berlin, 2004
              • [12]
                sheaves on affine flags and nilpotent cone of the Langlands dual group, electronic preprint Israel J. Math, to appear in
                • R. Bezrukavnikov Perverse
              • [13]
                Perverse coherent sheaves (after Deligne), electronic preprint
                • R. Bezrukavnikov
              • [14]
                Cohomology of tilting modules over quantum groups and t-structures on derived categories of coherent sheaves, to appear in Inv. Math
                • R. Bezrukavnikov
                • [15]
                  An equivalence between two categorical realization of the affine Hecke algebra, in preparation
                  • R. Bezrukavnikov
                  • [16]
                    Cherednik algebras and Hilbert schemes in characteristic p, electronic preprint to appear in Represent. Theory
                    • R. Bezrukavnikov
                      ,
                    • M. Finkelberg
                      ,
                    • V. Ginzburg
                  • [17]
                    equivalence for symplectic resolutions of quotient singularities, Tr. Mat. Inst. Steklova 246 (2004), Algebr. Geom. Metody, Svyazi i Prilozh., 20-42 translation in Proc. Steklov Inst. Math. 2004, no. 3 (246), 13-33
                    • R. Bezrukavnikov
                      ,
                    • D. Kaledin McKay
                    • [18]
                      quantization in positive characteristic, electronic preprint
                      • R. Bezrukavnikov
                        ,
                      • D. Kaledin Fedosov
                    • [19]
                      Localization of modules for a semisimple Lie algebra in prime characteristic, electronic preprint
                      • R. Bezrukavnikov
                        ,
                      • I. Mirkovic
                        ,
                      • D. Rumynin
                    • [19]
                      to appear in Annals of Math Singular localization and intertwining functors for semisimple Lie algebras in prime characteristic, electronic preprint , submitted to Nagoya
                      • Math. J
                    • [20]
                      Representable functors, Serre functors, and mutations, Izv. Ak. Nauk 35 (1990), no. 3, 519-541
                      • A. Bondal
                        ,
                      • M. Kapranov
                      • [21]
                        Derived categories of coherent sheaves, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 47-56, Higher Ed. Press, Beijing, 2002
                        • A. Bondal
                          ,
                        • D. Orlov
                        • [22]
                          categories of coherent sheaves report of ICM 2006, available as an electronic preprint
                          • T. Bridgeland Derived
                        • [23]
                          Stabilities on triangulated categories, electronic preprint to appear in Ann. Math
                          • T. Bridgeland
                        • 1-25 of 50
                        • 1
                        • 2
                        • 25 / page