Categories O for Dynkin Borel Subalgebras of Root-Reductive Lie Algebras

  • The purpose of my Ph.D. research is to define and study an analogue of the classical Bernstein-Gelfand-Gelfand (BGG) category O for the Lie algebra g, where g is one of the finitary, infinite-dimensional Lie algebras gl(∞,K), sl(∞,K), so(∞,K), and sp(∞,K). Here, K is an algebraically closed field of characteristic 0. We call these categories extended categories O and use the notation Ō. While the categories Ō are defined for all splitting Borel subalgebras of g, this research focuses on the categories Ō for very special Borel subalgebras of g which we call Dynkin Borel subalgebras. Some results concerning block decomposition and Kazhdan-Lusztig multiplicities carry over from usual categories O to our categories Ō. There are differences which we shall explore in detail, such as the lack of some injective hulls. In this connection, we study truncated categories Ō and are able to establish an analogue of BGG reciprocity in the categories Ō.

Download full text

Cite this publication

  • Export Bibtex
  • Export RIS

Citable URL (?):

Search for this publication

Search Google Scholar Search Catalog of German National Library Search OCLC WorldCat Search Catalog of GBV Common Library Network Search Catalog of Jacobs University Library Search Bielefeld Academic Search Engine
Meta data
Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Jacobs Univ.
Author:Thanasin Nampaisarn
Referee:Ivan Penkov, Alan Huckleberry, Vera Serganova
Advisor:Ivan Penkov
Persistent Identifier (URN):urn:nbn:de:gbv:579-opus-1007181
Document Type:PhD Thesis
Language:English
Date of Successful Oral Defense:2017/06/06
Date of First Publication:2017/07/29
Academic Department:Mathematics & Logistics
PhD Degree:Mathematics
Focus Area:Mobility
Call No:Thesis 2017/9

$Rev: 13581 $