The representations of the q-analogue of Brauer's centralizer algebras and the Kauffman polynomial of links (Q756774)

let C(\(\alpha\),q) denote the field of rational functions in two variables over C. The Kauffman polynomials of links are associated with a sequence of C(\(\alpha\),q) algebras denoted by \(C_ n(\alpha,q)\). The author constructs irreducible representations of \(C_ n(\alpha,q)\) which allow computations of the Kauffman polynomial. The algebras \(C_ n(\alpha,q)\) are one-dimensional deformations of Brauer's algebras \(D_ n(\beta)\), and \(\lim_{q\to 1}C_ n(q^{\beta /2},q)=D_ n(\beta)\).