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Acta Applicandae Mathematicae 21: 105-135, 1990. 105 © 1990 Kluwer Academic Publishers. Printed in the Netherlands. Combinatorial Algorithms for the Expansion of Various Products of Schur Functions by Jeffrey B. Remmel* Department of Mathematics, University of California, San Diego, U.S.A. AMS subject classifications (1980). 20B30, 20G05, 05Axx. Key words. Schur functions, combinatorics of Young tableaux. *Partially supported by NSP Grant #DMS 87-02473 106 JEFFREY B. REMMEL Introduction The main purpose of these lectures is first to briefly survey the fundamental con- nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod- ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful
Acta Applicandae Mathematicae – Springer Journals
Published: May 7, 2004
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