Structure of Thin Irreducible Modules of a Q-polynomial Distance-Regular Graph

Understand

Let Gamma be a Q-polynomial distance-regular graph with vertex set X, diameter D geq 3 and adjacency matrix A.

• Fix x in X and let A*=A*(x) be the corresponding dual adjacency matrix.
• Recall that the Terwilliger algebra T=T(x) is the subalgebra of Mat_X(C) generated by A and A*.
• Let W denote a thin irreducible T-module.