Properties of the Racahpolynomials with regard to the Lie algebrarepresentation of sl(2;C)

The Racah polynomial Rn(λ(x)) is a polynomial of degree n and is variable in λ(x). In this thesis two properties of this polynomial will be studied. One is the orthogonal property of the Racah polynomial. And the other is that the Racah polynomial can also be described as a polynomial of degree x and variable over λ(n). The Racah polynomials will be studied with the use of a representation of the Lie algebra of sl(2;C) and hypergeometric series. To do this, this Lie algebra will first be defined and then we will work towards defining the tensor product of three representations of the Lie algebra sl(2;C). From the tensor product, a series representation for the Racah polynomials will be found, which can be rewritten to a hypergeometric series. Then, the orthogonal property of sl(2;C) will be used to study the orthogonal property of the Racah polynomials. And the polynomial will be rewritten as a polynomial of degree x with the use of some identities of the hypergeometric series