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Multiplicities of Higher Lie Characters

Part of: Finite fields and commutative rings (number-theoretic aspects) Probabilistic theory: distribution modulo $1$; metric theory of algorithms Classical measure theory

Published online by Cambridge University Press:  09 April 2009

Manfred Schocker
Manfred Schocker
Affiliation:
Mathematical Institute24–29 St Giles Oxford OX1 3LBUK e-mail: schocker@maths.ox.ac.uk
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Abstract

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The higher Lie characters of the symmetric group Sn arise from the Poincaré-Birkhoff-Witt basis of the free associative algebra. They are indexed by the partitions of n and sum up to the regular character of Sn. A combinatorial description of the multiplicities of their irreducible components is given. As a special case the Kraśkiewicz-Weyman result on the multiplicities of the classical Lie character is obtained.

Keywords

symmetric groupgeneral linear groupfree Lie algebratableaumajor index.

MSC classification

Secondary: 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension 11T06: Polynomials 28A80: Fractals

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 1 , August 2003 , pp. 9 - 21
Copyright
Copyright © Australian Mathematical Society 2003

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