A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra

Askold M. Perelomov

Communications in Mathematics (2020)

  • Volume: 28, Issue: 3, page 301-305
  • ISSN: 1804-1388

Abstract

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For every simple finite-dimensional complex Lie algebra, I give a simple construction of all (except for the Pfaffian) basic polynomials invariant under the Weyl group. The answer is given in terms of the two basic polynomials of smallest degree.

How to cite

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Perelomov, Askold M.. "A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra." Communications in Mathematics 28.3 (2020): 301-305. <http://eudml.org/doc/297174>.

@article{Perelomov2020,
abstract = {For every simple finite-dimensional complex Lie algebra, I give a simple construction of all (except for the Pfaffian) basic polynomials invariant under the Weyl group. The answer is given in terms of the two basic polynomials of smallest degree.},
author = {Perelomov, Askold M.},
journal = {Communications in Mathematics},
keywords = {Weyl group; invariant polynomial},
language = {eng},
number = {3},
pages = {301-305},
publisher = {University of Ostrava},
title = {A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra},
url = {http://eudml.org/doc/297174},
volume = {28},
year = {2020},
}

TY - JOUR
AU - Perelomov, Askold M.
TI - A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 3
SP - 301
EP - 305
AB - For every simple finite-dimensional complex Lie algebra, I give a simple construction of all (except for the Pfaffian) basic polynomials invariant under the Weyl group. The answer is given in terms of the two basic polynomials of smallest degree.
LA - eng
KW - Weyl group; invariant polynomial
UR - http://eudml.org/doc/297174
ER -

References

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  2. Kostant, B., 10.2307/2372999, American Journal of Mathematics, 81, 1959, 973-1032, (1959) MR0114875DOI10.2307/2372999
  3. Macdonald, I.G., Orthogonal polynomials associated with root systems, Séminaire Lotharingien de Combinatoire, 45, 2000, B45a, (2000) MR1817334
  4. Mehta, M.L., 10.1080/00927878808823619, Communications in Algebra, 16, 5, 1988, 1083-1098, Taylor & Francis, (1988) MR0926338DOI10.1080/00927878808823619
  5. Onishchik, A.L., Vinberg, E.B., Lie groups and algebraic groups, 1990, Springer, (1990) MR1064110
  6. Racah, G., Sulla caratterizzazione delle rappresentazioni irriducibili dei gruppi semisemplici di Lie, Lincei-Rend. Sc. fis. mat. e nat, 8, 1950, 108-112, (1950) MR0035771
  7. Witt, E., Spiegelungsgruppen und aufz{ä}hlung halbeinfacher liescher Ringe, Abhandlungen aus dem mathematischen Seminar der Universit{ä}t Hamburg, 14, 1, 1941, 289-322, Springer, (1941) MR0005099

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