A commutative algebra on degenerate CP^1 and Macdonald polynomials

Understand

We introduce a unital associative algebra A over degenerate CP^1.

• We show that A is a commutative algebra and whose Poincar'e series is given by the number of partitions.
• Thereby we can regard A as a smooth degeneration limit of the elliptic algebra introduced by one of the authors and Odesskii.
• Then we study the commutative family of the Macdonald difference operators acting on the space of symmetric functions.