Front: [arXiv:0909.1860] Singular blocks of parabolic category O and finite W-algebras

Title: Singular blocks of parabolic category O and finite W-algebras
Authors: Ben Webster
Categories: math.RT Representation Theory (math.RA Rings and Algebras)
Comments: 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
MSC: 17B10, 81R10
Journal reference: J. Pure Appl. Algebra 215 (2011), no. 12, 2797-2804 (DOI 10.1016/j.jpaa.2011.03.020)

Abstract: 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.

Owner: Ben Webster
Version 1: Thu, 10 Sep 2009 02:29:47 GMT
Version 2: Tue, 6 Oct 2009 02:44:00 GMT
Version 3: Thu, 10 Dec 2009 04:01:18 GMT
Version 4: Thu, 27 Jan 2011 06:34:00 GMT