The Terwilliger Algebras Of Grassmann Graphs

Let Jq(n, m) denote the Grassmann graph with vertex set X and diameter min{m, n-m}. Fix a vertex x∈X. Let T= T(x) denote the Terwilliger algebra of Jq(n,m) corre-sponding to x. In this thesis, we give the structure of Terwilliger algebras of Grassmann graphs using the theory of Leonard pairs, quantum algebra Uq(sl2), and q-tetrahedron algebra (?)q.The thesis is composed of three chapters and organized as follows:In chapter 1, we introduce the notions of Leonard pairs and Leonard systems, quan-tum algebra Uq(sl2), q-tetrahedron algebra (?)q, distance-regular graphs and some related properties.In chapter 2, we introduce the Leonard systems that have dual q-Hahn type and give related Uq(sl2)-module structure and (?)g-module structure.In chapter 3, we display the Terwilliger algebras of Grassmann graphs using the theory of quantum algebra Uq(sl2) and q-tetrahedron algebra (?)q.