Basic representations of A2l⁽²⁾and Dl+1⁽²⁾and the polynomial solutions to the reduced BKP hierarchies

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 the Maya game.