Abstract
The one-variable non-symmetric Wilson polynomials are shown to coincide with the BannaiâIto polynomials. The isomorphism between the corresponding degenerate double affine Hecke algebra of type $(C_1^{\vee }, C_1)$ and the BannaiâIto algebra is established. The BannaiâIto polynomials are seen to satisfy an orthogonality relation with respect to a positive-definite and continuous measure on the real line. A non-compact form of the BannaiâIto algebra is introduced and a four-parameter family of its infinite-dimensional and self-adjoint representations is exhibited.
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