A note on Cauchy's formula

Abstract

We use the correlation functions of vertex operators to give a proof of Cauchy's formulaAs an application of the interpretation, we obtain an expansion of ∞ i=1 (1 − q i ) i−1 in terms of half plane partitions.gave a physical interpretation of the limit of (1.1) using plane partitions, and the underlying algebraic structure is an infinite dimensional Heisenberg algebra with central charge 1. This is partly based on the vertex operator approach to symmetric functions [8,9].In [11], charged free bosonic system provides a different Heisenberg algebra with central charge. .] (resp. the dual space V * ) of the Heisenberg algebra H generated by the vacuum vector |0 (resp. dual vacuum 0|), we can introduce the fermionic field φ(z) to obtain a base {|λ } of V MSC (2010): Primary: 05E05; Secondary: 17B37.