2009/09/30 by Ben Webster · 20 citations
Engineering · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Algorithm #Engineering #Homotopy and Cohomology in Algebraic Topology #Mathematics #Mechanical engineering #Scroll #math.RA #math.RT #msc:17B10 #msc:81R10
paper · pdf · doi:10.1016/j.jpaa.2011.03.020
published in Journal of Pure and Applied Algebra 215(12), 2797-2804 (Elsevier BV) · 12 pages; v2 and v3: minor corrections suggested by referee; statement of some results changed; v4: additional material added on connection to Slodowy slices and rewrite of introduction
arxiv created 2011/01/27 · openalex publication_date 2011/04/14 · arxiv updated 2014/12/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that each integral infinitesimal block of parabolic category O (including singular ones) for a semi-simple Lie algebra can be realized as a full subcategory of a "thick" category O over a finite W-algebra for the same Lie algebra. The nilpotent used to construct this finite W-algebra is determined by the central character of the block, and the subcategory taken is that killed by a two-sided ideal depending on the original parabolic. The equivalences in question are induced by those of Milicic-Soergel and Losev. We also give a proof of a result of some independent interest: the singular blocks of parabolic category O can be geometrically realized as "partial Whittaker sheaves" on partial flag varieties.