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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generalised Vandermonde determinants and Schur functions
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by R. C. King PDF
Proc. Amer. Math. Soc. 48 (1975), 53-56 Request permission

Abstract:

A formula for determinants similar to that of Vandermonde is given in terms of the Vandermonde determinant and Schur functions. The Schur functions are then expressed in terms of symmetric monomial functions.
References
  • A. M. Fink, Certain determinants related to the Vandermonde, Proc. Amer. Math. Soc. 38 (1973), 483–488. MR 311677, DOI 10.1090/S0002-9939-1973-0311677-7
  • I. Schur, Über eine Klasse von Matrizen die sich einer gegebenen Matrix zuordnen lassen, Inaugural Dissertation, Berlin, 1901. D. E. Littlewood, The theory of group characters, 2nd ed., University Press, Oxford, 1950. F. D. Murnaghan, The theory of group representation, Johns Hopkins Press, Baltimore, Md., 1938.
  • G. de B. Robinson, Representation theory of the symmetric group, Mathematical Expositions, No. 12, University of Toronto Press, Toronto, 1961. MR 0125885
  • Stephen Blaha, Character analysis of $\textrm {U}(N)$ and $\textrm {SU}(N)$, J. Mathematical Phys. 10 (1969), 2156–2168. MR 255149, DOI 10.1063/1.1664816
  • R. C. King and S. P. O. Plunkett, The evaluation of branching rules for linear groups using mappings between weight spaces, J. Phys. 33 (1972), 145-153. D. E. Littlewood and A. R. Richardson, Group characters and algebra, Philos. Trans. Roy. Soc. London A233 (1934), 99-141. T. Muir, Theory of determinants, Vols. (i), (ii), (iii) and (iv), Macmillan, London, 1906.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 53-56
  • MSC: Primary 15A15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0371919-0
  • MathSciNet review: 0371919