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Discrete Mathematics and Combinatorics
UNF Graduate Theses and Dissertations
Dissertations, Academic -- UNF -- Master of Science in Mathematical Science
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The Lie Algebra Sl2(C) And Krawtchouk Polynomials, Nkosi Alexander
The Lie Algebra Sl2(C) And Krawtchouk Polynomials, Nkosi Alexander
UNF Graduate Theses and Dissertations
The Lie algebra L = sl2(C) consists of the 2 × 2 complex matrices that have trace zero, together with the Lie bracket [y, z] = yz − zy. In this thesis we study a relationship between L and Krawtchouk polynomials. We consider a type of element in L said to be normalized semisimple. Let a, a^∗ be normalized semisimple elements that generate L. We show that a, a^∗ satisfy a pair of relations, called the Askey-Wilson relations. For a positive integer N, we consider an (N + 1)-dimensional irreducible L-module V consisting of the homogeneous polynomials in two variables …