Dual polar graphs, the quantum algebra U_q(sl_2), and Leonard systems of dual q-Krawtchouk type

Understand

In this paper we consider how the following three objects are related: (i) the dual polar graphs; (ii) the quantum algebra U_q(sl_2); (iii) the Leonard systems of dual q-Krawtchouk type.

• For convenience we first describe how (ii) and (iii) are related.
• For a given Leonard system of dual q-Krawtchouk type, we obtain two U_q(sl_2)-module structures on its underlying vector space.
• We now describe how (i) and (iii) are related.