Graduation Semester and Year

2014

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dimitar Grantcharov

Abstract

A long-standing problem in representation theory is the classification of all simple weight modules of the classical Lie superalgebras. This problem was reduced to the classification of simple bounded highest weight modules. The latter classification has been accomplished for all classical Lie superalgebras except for the orthosymplectic series osp(m|2n) where m = 1, 3, 4, 5, 6. In this thesis, we complete the classification of the simple bounded highest weight modules of osp(1|2n) (i.e., for m = 1). The classification is obtained by developing constraints on primitive vectors in tensor products of bounded (Weyl) and finite-dimensional osp(1|2n)-modules.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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Mathematics Commons

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