Applications of Minor-Summation Formula I. Littlewoodʹs Formulas Original Research Article

The first and the third authors obtained a minor-summation formula of Pfaffian, which expresses a weighted sum of minors of any rectangular matrix in terms of a single Pfaffian. In this paper, as an application of this minor-summation formula, we give a new proof of Littlewoodʹs formulas with additional parameters and generalize them for the classical groups.