The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and U(sl2)

The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces an abelian automorphism subgroup is shown act as weighted subspace lattice. connection between latter and Uq(sl2) used find irreducible components standard module Terwilliger algebra graphs. multiplicities isomorphic submodules are given.