Schur Functions and Affine Lie Algebras
Résumé
We make use of the representation theory of the infinite-dimensional Lie $ algebras a , b , and sl to derive explicit formulas relating Schur's P-functions to ϱ ϱ 2 Schur's S-functions. ᮊ 1998 Academic Press 2 n n n w x of ᑭ isomorphic to the hyperoctaedral group 35 .
2 n Ž As discovered by the Kyoto school Sato, Date, Jimbo, Kashiwara, . Miwa , the interpretation in terms of hierarchies of partial differential equations can be reformulated in the framework of infinite-dimensional $ w x Lie algebras 11 . Indeed, the basic representations of a s gl and b ϱ ϱ ϱ $ s go can be realized in the vector spaces spanned by S-functions and ϱ 103