Simple Weight Modules of the Lie Algebra of Vector Fields of C2

Author

Andrew Cavaness

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dimitar Grantcharov

Abstract

Classification of the weight modules of the Lie algebra Wn of vector fields on C n has been a long-standing problem in the area of representation theory. In this thesis, a classification of all simple weight modules of W2 with a uniformly bounded set of weight multiplicities is provided, and much of the theory that will be needed to classify all simple weight modules of Wn with a uniformly bounded set of weight multiplicities will also be developed. To achieve this classification, a new family of generalized tensor Wn-modules is introduced, and a twisted localization functor is applied.

Keywords

Lie algebra, Weight module, Twisted localization, Parabolic induction, Tensor module

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Cavaness, Andrew, "Simple Weight Modules of the Lie Algebra of Vector Fields of C2" (2017). Mathematics Dissertations. 221.
https://mavmatrix.uta.edu/math_dissertations/221