This thesis consists of a summary and three papers, concerning some aspects of representation theory for complex finite dimensional semi-simple Lie algebras with focus on the BGG-category O. Paper I is motivated by the many useful properties of functors on category O given by tensoring with finite dimensional modules, such as projective functors and translation functors. We study properties of functors on O given by tensoring with arbitrary (possibly infinite dimensional) modules. Such functors give rise to a faithful action of O on itself via exact functors which preserve tilting modules, via right exact functors which preserve projective modules, and via left exact functors which preserve injective modules…
Contents
1 Introduction
1.1 The BGG category O
1.2 Tensor products
1.3 Kostant’s problem
2 Summary of papers
2.1 Paper I
2.2 Paper II
2.3 Paper III
Summary in Swedish
Acknowledgements
Bibliography
Author: Kahrstrom, Johan
Source: Uppsala University Library
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