Categorical cell decomposition of quantized symplectic algebraic varieties

Article, Preprint, Other literature type English OPEN
Bellamy, Gwyn; Dodd, Christopher; McGerty, Kevin; Nevins, Thomas;
(2017)
  • Publisher: Mathematical Sciences Publishers
  • Journal: issn: 1465-3060
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.2140/gt.2017.21.2601
  • Subject: Mathematics - Symplectic Geometry | 14F05 | symplectic | 53D55 | Mathematics - Algebraic Geometry | elliptic | Mathematics - Quantum Algebra | quantization
    arxiv: Mathematics::Symplectic Geometry | Mathematics::Category Theory

We prove a new symplectic analogue of Kashiwara’s equivalence from D–module\ud theory. As a consequence, we establish a structure theory for module categories over\ud deformation-quantizations that mirrors, at a higher categorical level, the BiałynickiBirula\ud stratifi... View more
  • References (20)
    20 references, page 1 of 2

    [1] K Ardakov, S Wadsley, On irreducible representations of compact p -adic analytic groups, Ann. of Math. 178 (2013) 453-557 MR

    [2] M Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 23-58 MR

    [3] A Be˘ılinson, J Bernstein, A proof of Jantzen conjectures, from “I M Gel'fand seminar” (S Gindikin, editor), Adv. Soviet Math. 16, Amer. Math. Soc., Providence, RI (1993) 1-50 MR

    [8] R V Bezrukavnikov, D B Kaledin, McKay equivalence for symplectic resolutions of quotient singularities, Tr. Mat. Inst. Steklova 246 (2004) 20-42 MR In Russian; translated in Proc. Steklov Inst. Math. 246 (2004) 13-33

    [25] V Ginzburg, Harish-Chandra bimodules for quantized Slodowy slices, Represent. Theory 13 (2009) 236-271 MR

    [26] I G Gordon, I Losev, On category O for cyclotomic rational Cherednik algebras, J. Eur. Math. Soc. 16 (2014) 1017-1079 MR

    [27] I G Gordon, J T Stafford, The Auslander-Gorenstein property for Z-algebras, J. Algebra 399 (2014) 102-130 MR

    [28] A Grothendieck, Eléments de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents, I, Inst. Hautes Études Sci. Publ. Math. 11 (1961) 5-167 MR

    [29] V Guillemin, S Sternberg, Symplectic techniques in physics, 2nd edition, Cambridge University Press (1990) MR

    [30] R Hartshorne, On the De Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. 45 (1975) 5-99 MR

  • Metrics
Share - Bookmark