\[normlps1\] or \[normlps2\]; then pick up the corresponding normalized Askey-Wilson relations in Lemmas \[awnormals\], \[awnormals1\] or \[awnormals2\]; and then apply the inverse affine transformation to the normalized relations using formula (\[newaw\]). This procedure can be applied for any $d$, although for $d<3$ the type of a representing parameter array is ambiguous and the Askey-Wilson relations are not unique.

For the rest of this section, we refer to the results of Sections \[qpararrays2\] and \[otherpararrays\]. We assume $d\le 3$ and adopt the following terminology. A pair of Askey-Wilson relations is called [*normalized*]{} if it satisfies the specifications of Lemma \[normrules\] and the description in the previous section; see (\[scalingpars\]) and (\[scnormal\]). A Leonard pair is [*normalized*]{} if it satisfies normalized Askey-Wilson relations. A parameter array is [*normalized*]{} if it can be expressed in one of the forms of Lemma \[normlps1\] or Lemma \[normlps2\].

We consider the following questions:

\[question0\] How unique is normalization of Askey-Wilson relations?

\[question1\] Given a Leonard pair, how unique is its normalization?

\[question4\] Is every normalized Leonard pair representable by a normalized parameter array?

\[question2\] Are normalized parameter arrays represented uniquely by the forms in Lemmas \[awnormals1\] and \[awnormals2\]?

\[question3\] Do the relation operators $\downarrow$, $\Downarrow$, $\downarrow\Downarrow$ 