On the Jacobian Matrices of Generalized Chebyshev Polynomials

İleri A., KÜÇÜKSAKALLI Ö.

Journal of Lie Theory, vol.35, no.1, pp.1-16, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 1
  • Publication Date: 2025
  • Journal Name: Journal of Lie Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1-16
  • Keywords: character formula, Exponential invariants
  • Middle East Technical University Affiliated: Yes

Abstract

We give a practical method to compute the Jacobian matrices of generalized Chebyshev polynomials associated to arbitrary semisimple Lie algebras. The entries of each Jacobian matrix can be expressed as a linear combination of characters of irreducible representations of the underlying Lie algebra with integer coefficients. These integer coefficients can be obtained by basic computations in the fundamental Weyl chamber.