Graduation Semester and Year
Fall 2024
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Dr. Dimitar Grantcharov
Second Advisor
Dr. Ruth Gornet
Third Advisor
Dr. David Jorgensen
Fourth Advisor
Dr. Theresa Jorgensen
Fifth Advisor
Dr. Michaela Vancliff
Abstract
This thesis studies generalized Laurent polynomial representations of the general linear Lie algebra. These representations arise naturally as representations over the Weyl algebra consisting of differential operators on $\mathbb{C}^n$. Our main result is an explicit description of the socle filtration of $P_{\mu} = \Span \{x^{\bf m} \: | \: {\bf m} \in \mathbb Z^{n}, \: | \bf{m} | \: = \mu \}$ for $\mu \in \mathbb{Z}$.
Keywords
Lie Algebra, Representation Theory, Weyl Representation, Socle Filtratation
Disciplines
Algebra
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
Hernandez Garcia, Amairani, "On Weyl Representations of gl(n)" (2024). Mathematics Dissertations. 256.
https://mavmatrix.uta.edu/math_dissertations/256