Hypertoric category O

被引：37

作者：

Braden, Tom ^{[1
]}

Licata, Anthony ^{[2
]}

Proudfoot, Nicholas ^{[3
]}

Webster, Ben ^{[3
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[2] Stanford Univ, Dept Math, Palo Alto, CA 94305 USA

[3] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

ADVANCES IN MATHEMATICS | 2012年 / 231卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Enveloping algebras; Category O; Quantization; Localization; KOSZUL DUALITY; G-MODULES; ALGEBRAS; FUNCTORS; VARIETIES; GEOMETRY;

D O I：

10.1016/j.aim.2012.06.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the representation theory of the invariant subalgebra of the Weyl algebra under a torus action, which we call a "hypertoric enveloping algebra". We define an analogue of BGG category O for this algebra, and identify it with a certain category of sheaves on a hypertoric variety. We prove that a regular block of this category is highest weight and Koszul, identify its Koszul dual, compute its center, and study its cell structure. We also consider a collection of derived auto-equivalences analogous to the shuffling and twisting functors for BGG category O. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1487 / 1545

页数：59

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