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On the Wall polynomials and the L-M-W conjectures

Published online by Cambridge University Press:  09 April 2009

George E. Andrews
George E. Andrews
Affiliation:
The Pennsylvania State UniversityUniversity Park, Pennsylvania, U.S.A.
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Abstract

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This paper provides explicit formulas for the Wall polynomials which arise in Wall's work on conjugacy classes in the unitary, symplectic and orthogonal groups. From these explicit formulas are easily derived six interesting limiting idetities incuding the two that arise in the Luszing-Macdonald Wall conjectures.

Keywords

q-seriesGaussian polynomialsWall polynomialsgroup theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 17 - 26
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Andrews, G. E., ‘The theory of partitions,’ Encyclopedia of mathematics and its applications, Vol. 2 (Addison-Wesley, Reading, Mass., 1976).Google Scholar
[2]Andrews, G. E., ‘Partitions, q-series, and the Lusztig-Macdonald-Wall conjectures,’ Invent. Math. 41 (1977), 91–102.CrossRefGoogle Scholar
[3]Garsia, A. and Remmel, J., ‘A combinatorial view of Andrews' proof of the L-M-W conjectures,’ European J. Combin., to appear.Google Scholar
[4]Lusztig, G., ‘Irreducible representations of finite classical groups,’ Invent. Math. 43 (1977), 125–177.CrossRefGoogle Scholar
[5]Wall, G. E., ‘On the conjugacy classes in the unitary, symplectic and orthogonal groups,’ J. Austral. Math. Soc. 3 (1963), 1–62.CrossRefGoogle Scholar