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

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

This video was recorded at 6th Slovenian International Conference on Graph Theory, Bled 2007. 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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