A study of q-analogues of symmetric spaces in the framework of association schemes

它是关于P-和Q-多项式计划的Terwilliger代数，一个特征公式保持其不可约表示，反过来，他们的不可约表示有一个结构，对应于分解的特征公式。已知该猜想对于类型I的情况是正确的，并且对于其余的情况是开放的，即，第二、三类案件。本文证明了II、III型TD-偶是L-偶的某种张量积，从而肯定地解决了这一猜想。结果表明，特征标公式不仅对I型TD偶成立，而且对II、III型TD偶也成立。

It is conjectured about the Terwilliger algebras of P- and Q-polynomoial schemes that a character formula holds for their irreducible representations, and in turn that their irreducible representations have a structure that corresponds to the decomposition of the character formula. This conjecture was known to be true for the case of type I and left open for the remaining cases, i.e., the cases of type II, III. In this study, we have settled the conjecture affirmatively by showing TD-pairs of type II, III are certain kind of tensor products of L-pairs. As a result, it is shown that a character formula holds not only for TD-pairs of type I, but also for those of type II, III.