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- Academic -- UNF -- Master of Science in Mathematical Science; Dissertations (1)
- Academic -- UNF -- Mathematics; algebra; hypercube; terwilliger; subconstituent (1)
- Dissertations, Academic -- UNF -- Master of Science in Mathematical Science (1)
- Dissertations, Academic -- UNF -- Mathematics (1)
- Krawtchouk polynomials (1)
Articles 1 - 2 of 2
Full-Text Articles in Algebra
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 …
The Subconstituent Algebra Of A Hypercube, Jared B. Billet
The Subconstituent Algebra Of A Hypercube, Jared B. Billet
UNF Graduate Theses and Dissertations
We study the hypercube and the associated subconstituent algebra. Let Q_D denote the hypercube with dimension D and let X denote the vertex set of Q_D. Fix a vertex x in X. We denote by A the adjacency matrix of Q_D and by A* = A*(x) the diagonal matrix with yy-entry equal to D − 2i, where i is the distance between x and y. The subconstitutent algebra T = T(x) of Q_D with respect to x is generated by A and A* . We show that A 2A* − 2AA*A + A*A 2 = 4A* A*2A − 2A*AA* + …