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Schur Functions and Affine Lie Algebras

✍ Scribed by Bernard Leclerc; Séverine Leidwanger

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
347 KB
Volume
210
Category
Article
ISSN
0021-8693

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✦ Synopsis

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

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