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

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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