On the Jacobian Matrices of Generalized Chebyshev Polynomials
Journal of Lie Theory, vol.35, no.1, pp.1-16, 2025 (SCI-Expanded, Scopus)
- 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.