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Multiplicity-free quotient tensor algebras

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

G. E. Wall
G. E. Wall
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
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Abstract

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Let V be an infinite-dimensional vector space ovre a field of characteristic 0. It is well known that the tensor algebra T on V is a completely reducible module for the general linear group G on V. This paper is concerned with those quotient algebras A of T that are at the same time modules for G. A partial solution is given to the problem of determinig those A in which no irreducible constitutent has multiplicity greater thatn 1.

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 279 - 298
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Dixmier, J., Enveloping algebras (North-Holland, Amsterdam, 1977).Google Scholar
[2]Inglis, N. F. J., Richardson, R. W. and Saxl, J., ‘An explicit model for the complex representations of Sn’, Arch. Math. 54 (1990), 258–259.CrossRefGoogle Scholar
[3]Kljačko, A. A., ‘Models for complex representations of the groups GL(n, q) adn Weyl groups’, Soviet Math. Doklady 24 (1981), 496–499.Google Scholar
[4]Macdonald, I. G., Symmetric functions and Hall polynomials, 2nd edition (Oxford University Press, Oxford, 1994).Google Scholar
[5]Wall, G. E., ‘A note on multiplicity-free tensor representations’, J. Pure Appl. Algebra 88 (1993), 249–263.CrossRefGoogle Scholar
[6]Wall, G. E., ‘More on multiplicty-free tensor representations’, Research report 95–29, (School of Mathematics and Statistics, University of Sydney, 1995).Google Scholar