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\nvectors are represented in terms of Schur's $Q$-functions. The method to get\nthe polynomial solutions to the reduced BKP hierarchies is shown to be\nequivalent to a certain rule in Maya game.\n