Operator Product Formula for a Special Macdonald Function

Abstract

In this paper, we construct two sets of vertex operators S + and S ? from a direct sum of two sets of Heisenberg algebras. Then by calculating the vacuum expectation value of some products of vertex operators, we get Macdonald function in special variables x i = t i- 1 ( i = 0,1, 2, ). Hence we obtain the operator product formula for a special Macdonald function P λ (1, t , , t n-1 ; q , t ) when n is finite as well as when n goes to infinity.