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The Schur function realization of vertex operators. (English) Zbl 0774.17031
Summary: We present a realization of untwisted vertex operators in terms of operations on Schur functions. Calculations of matrix elements and traces of products of vertex operators are performed using results from the classical theory of symmetric functions. The concepts of compound, composite and supersymmetric Schur functions naturally appear in this context. Furthermore, a trace formula for a product of vertex operators turns out to be a generalization of a Macdonald identity reformulated in terms of Schur functions.

MSC:
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
05E05 Symmetric functions and generalizations
81T05 Axiomatic quantum field theory; operator algebras
22E70 Applications of Lie groups to the sciences; explicit representations
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