  We consider a bipartite distance-regular graph $G$ with diameter $D$ at least
4 and valency $k$ at least 3. We obtain upper and lower bounds for the local
eigenvalues of $G$ in terms of the intersection numbers of $G$ and the
eigenvalues of $G$. Fix a vertex of $G$ and let $T$ denote the corresponding
subconstituent algebra. We give a detailed description of those thin
irreducible $T$-modules that have endpoint 2 and dimension $D-3$. In an earlier
paper the first author defined what it means for $G$ to be taut. We obtain
three characterizations of the taut condition, each of which involves the local
eigenvalues or the thin irreducible $T$-modules mentioned above.

Combinatorics;Representation Theory