in loc. cit., due to the numbering of roots explained below. Comparing (4.0.1)
and the specialization Table 1.0.1, we find that (4.0.1) is included as the
case $t_{m}=t_{l}^{2}=t_{s}=t$ in the $BC_{n}$ specialization of §2.4.4:

| $t$ | $t_{0}$ | $t_{n}$ | $u_{0}$ | $u_{n}$
---|---|---|---|---|---
$BC_{n}$ | $t_{m}$ | $t_{l}^{2}$ | $t_{s}$ | $1$ | $t_{s}$

Let us write again the Dynkin diagram (2.4.43) of the affine root system of
type $BC_{n}$:

$\displaystyle\dynkin[mark=o,edgelength=.75cm,reversearrows,labels={},labels*={0,1,2,,,n-1,n}]A[2]{even}$
(4.0.2)

This is in fact the Dynkin diagram for the affine Lie algebra of type
$A^{(2)}_{n}$ for even $n$ [Ka90, p.55, §4.8, Table Aff 2], with the numbering
of the roots $0,1,\dotsc,n$ reversed. Thus, very naively speaking, we can read
the result of Ion on the Koornwinder specialization [I03, §3] from our
specialization Table 1.0.1.

Acknowledgements. The authors thank Professor Masatoshi Noumi for valuable
comments. In particular, Remarks 2.3.2 and 2.4.2 are added as a result of the
correspondences with him.

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