純粋・応用数学研究センター

組合せ論セミナー

Jae-Ho Lee（東北大学）「Q-polynomial distance-regular graphs and a double affine Hecke algebra of rank one」

The concept of a Q-polynomial distance-regular graph (DRG) was introduced by Delsarte in 1973. Since then, this concept has been linked to other areas, such as coding theory and Lie theory. The double affine Hecke algebra (DAHA) was introduced by Cherednik in 1992. The theory of the DAHA has been connected to many other areas of mathematics, such as algebraic geometry, Lie theory, and orthogonal polynomials. I have discovered a relationship between Q-polynomial DRGs and a certain DAHA of rank one. In this presentation, we will display a certain module for a DAHA of rank one. Using this module we will show how Q-polynomial DRGs and the DAHA are related. This talk is based on my dissertation work.