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Further determinant identities related to classical root systems

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Abstract

By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems.

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References

  1. G. Bhatnagar: A short proof of an identity of Sylvester. Int. J. Math. Math. Sci. 22 (1999), 431–435.

    Article  MathSciNet  MATH  Google Scholar 

  2. W. Chu: Divided differences and symmetric functions. Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 2 (1999), 609–618.

    MathSciNet  MATH  Google Scholar 

  3. W. Chu: Determinants and algebraic identities associated with the root systems of classical Lie algebras. Commun. Algebra 42 (2014), 3619–3633.

    Article  MathSciNet  MATH  Google Scholar 

  4. W. Chu, L. V. Di Claudio: The Vandermonde determinant and generalizations associated with the classical Lie algebras. Ital. J. Pure Appl. Math. 20 (2006), 139–158. (In Italian.)

    MathSciNet  MATH  Google Scholar 

  5. F. J. Dyson: Statistical theory of the energy levels of complex systems. I. J. Math. Phys. 3 (1962), 140–156.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. Fulton, J. Harris: Representation Theory. Graduate Texts in Mathematics 129, Springer, New York, 1991.

    Google Scholar 

  7. I. J. Good: Short proof of a conjecture by Dyson. J. Math. Phys. 11 (1970), 1884.

    Article  MathSciNet  Google Scholar 

  8. K. I. Gross, D. St. P. Richards: Constant term identities and hypergeometric functions on spaces of Hermitian matrices. J. Stat. Plann. Inference 34 (1993), 151–158.

    Article  MathSciNet  MATH  Google Scholar 

  9. I. G. Macdonald: Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs, Clarendon Press, Oxford, 1979.

    Google Scholar 

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Correspondence to Wenchang Chu.

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Chu, W. Further determinant identities related to classical root systems. Czech Math J 67, 981–987 (2017). https://doi.org/10.21136/CMJ.2017.0265-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0265-16

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