Distance-regular graphs and the quantum affine algebra Uq(bsl2)

author: Paul Terwilliger, University of Wisconsin - Madison
published: Sept. 7, 2007,   recorded: September 2007,   views: 4325

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Combinatorial objects, such as graphs, can often be used to construct representations of abstract algebras. In this talk we will consider a graph possessing a high degree of regularity, known as a distance-regularity. For this graph we define an algebra generated by the adjacency matrix and a certain diagonal matrix. There exists a set of elements in this algebra that, under a minor assumption, satisfy some attractive relations. Using these relations we obtain a representation of the quantum affine sl2 algebra.

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