# Q-polynomial distance-regular graphs and nonsymmetric Askey-Wilson polynomials

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Jae Ho Lee

Tohoku University

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**Minisymposium:**
ASSOCIATION SCHEMES

**Content:**
Nonsymmetric Askey-Wilson polynomials were defined by Sahi in 1999. Roughly speaking, they are the eigenfunctions of the Cherednik-Dunkl operator and form a linear basis of the space of the Laurent polynomials in one variable. In my thesis (2013), we found a relationship between $Q$-polynomial distance-regular graphs and a double affine Hekce algebra of rank one. In this talk, using this relationship we will define some nonsymmetric Laurent polynomials and discuss how these polynomials are related with Sahi's nonsymmetric Askey-Wilson polynomials.