solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看8437次
Dualities in the $q$-Askey scheme and degenerated DAHA. (arXiv:1803.02775v1 [math.CA])
来源于:arXiv
The Askey-Wilson polynomials are a four-parameter family of orthogonal
symmetric Laurent polynomials $R_n[z]$ which are eigenfunctions of a
second-order $q$-difference operator $L$, and of a second-order difference
operator in the variable $n$ with eigenvalue $z + z^{-1}=2x$. Then $L$ and
multiplication by $z+z^{-1}$ generate the Askey-Wilson (Zhedanov) algebra. A
nice property of the Askey-Wilson polynomials is that the variables $z$ and $n$
occur in the explicit expression in a similar and to some extent exchangeable
way. This property is called duality. It returns in the non-symmetric case and
in the underlying algebraic structures: the Askey-Wilson algebra and the double
affine Hecke algebra (DAHA). In this paper we follow the degeneration of the
Askey-Wilson polynomials until two arrows down and in four diferent situations:
for the orthogonal polynomials themselves, for the degenerate Askey-Wilson
algebras, for the non-symmetric polynomials and for the (degenerate) DAHA and
its re 查看全文>>