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.

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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
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

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