Further determinant identities related to classical root systems

Wenchang Chu

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 4, page 981-987
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Chu, Wenchang. "Further determinant identities related to classical root systems." Czechoslovak Mathematical Journal 67.4 (2017): 981-987. <http://eudml.org/doc/294183>.

@article{Chu2017,
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.},
author = {Chu, Wenchang},
journal = {Czechoslovak Mathematical Journal},
keywords = {Vandermonde determinant; symmetric function; classical root system},
language = {eng},
number = {4},
pages = {981-987},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Further determinant identities related to classical root systems},
url = {http://eudml.org/doc/294183},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Chu, Wenchang
TI - Further determinant identities related to classical root systems
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 981
EP - 987
AB - 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.
LA - eng
KW - Vandermonde determinant; symmetric function; classical root system
UR - http://eudml.org/doc/294183
ER -

References

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  2. Chu, W., Divided differences and symmetric functions, Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 2 (1999), 609-618. (1999) Zbl0935.05088MR1719558
  3. Chu, W., 10.1080/00927872.2013.790394, Commun. Algebra 42 (2014), 3619-3633. (2014) Zbl1291.05208MR3196066DOI10.1080/00927872.2013.790394
  4. Chu, W., Claudio, L. V. Di, The Vandermonde determinant and generalizations associated with the classical Lie algebras, Ital. J. Pure Appl. Math. 20 (2006), 139-158 Italian. (2006) Zbl1150.15005MR2247418
  5. Dyson, F. J., 10.1063/1.1703773, J. Math. Phys. 3 (1962), 140-156. (1962) Zbl0105.41604MR0143556DOI10.1063/1.1703773
  6. Fulton, W., Harris, J., 10.1007/978-1-4612-0979-9, Graduate Texts in Mathematics 129, Springer, New York (1991). (1991) Zbl0744.22001MR1153249DOI10.1007/978-1-4612-0979-9
  7. Good, I. J., 10.1063/1.1665339, J. Math. Phys. 11 (1970), 1884. (1970) MR0258644DOI10.1063/1.1665339
  8. Gross, K. I., Richards, D. St. P., 10.1016/0378-3758(93)90040-D, J. Stat. Plann. Inference 34 (1993), 151-158. (1993) Zbl0767.33010MR1209996DOI10.1016/0378-3758(93)90040-D
  9. Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Clarendon Press, Oxford (1979). (1979) Zbl0487.20007MR0553598

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