Abstract
In a series of papers, Date, Jimbo, Kashiwara and Miwa (DJKM) studied soliton equations using representation of Lie algebras. In particular, they found a remarkable new hierarchy of KP type, namely BKP. One can also study the same problem using vertex operators for the infinite rank affine Lie algebras a ∞, b ∞. Combining the ideas of Kac and DJKM, we found the realization of the basic representation and the half spin representations for d ∞ as well. In particular, we show that DKP and BKP are essentially the same, moreover, one gets a modified DKP hierarchy.
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