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Functional realization of basic representations of factorizable Lie groups and algebras. (English. Russian original) Zbl 0577.17011

Funct. Anal. Appl. 19, 193-206 (1985); translation from Funkts. Anal. Prilozh. 19, No. 3, 36-52 (1985).
The main results with proofs of the author’s notes devoted to the adèle approach in soliton theory and in the theory of Kac-Moody algebras are stated. The two definitions of the \(\tau\)-function as a spherical function (”matrix element”) and as modular co-form (”infinite determinant”) are given. The key result (variant of the Frobenius duality theorem) is its coincidence.
Reviewer: A.K.Guch

MSC:

17B65 Infinite-dimensional Lie (super)algebras
14L35 Classical groups (algebro-geometric aspects)
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
35Q99 Partial differential equations of mathematical physics and other areas of application
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