Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies

Abstract

Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight vectors are represented in terms of Schur's $Q$-functions. The method to get the polynomial solutions to the reduced BKP hierarchies is shown to be equivalent to a certain rule in Maya game.