BASES OF INFINITE-DIMENSIONAL REPRESENTATIONS OF ORTHOSYMPLECTIC LIE SUPERALGEBRAS

Author

Dwight Anderson Williams II

Graduation Semester and Year

2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dimitar Grantcharov

Abstract

We provide explicit bases of representations of the Lie superalgebra osp(1|2n) obtained by taking tensor products of infinite-dimensional representation and the standard representation. This infinite-dimensional representation is the space of polynomials C[x₁,...,xn]. Also, we provide a new differential operator realization of osp(1|2n) in terms of differential operators of n commuting variables x₁,...,xn and 2n anti-commuting variables ξ1; : : : ; ξ2n.

Keywords

Algebra, Lie superalgebras, Supermathematics, Representation theory, Orthosymplecitc

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

Williams II, Dwight Anderson, "BASES OF INFINITE-DIMENSIONAL REPRESENTATIONS OF ORTHOSYMPLECTIC LIE SUPERALGEBRAS" (2020). Mathematics Dissertations. 169.
https://mavmatrix.uta.edu/math_dissertations/169