A formula for two-row Macdonald functions (Q1196412)

Let \(Q_ \lambda\) be the usual Macdonald symmetric functions. The goal of the present work is to prove the following result. Theorem. If \(\lambda\) is a partition with two parts \(r\) and \(s,r\geq s\geq 0\), then \[ Q_{r,s}=\sum^ s_{i=0}a^ p_ iQ_{r+i}Q_{s-i} \] where \(p=r-s\), \(a^ p_ 0=1\), and for \(i>0\) \[ a^ p_ i={(t- 1)\cdots(t-q^{i-1})\over(1-q)\cdots(1-q^ i)}\cdot{(1-q^{p+1})\cdots (1-q^{p+i-1})(1-q^{p+2i})\over(1-q^{p+1}t)\cdots(1-q^{p+i}t)}. \]