Journal of Lie Theory

no. 1
On the Jacobian Matrices of Generalized Chebyshev Polynomials
Ahmet Ileri1; Ömer Kücüksakalli1
1Dept. of Mathematics, Middle East Technical University, Ankara, Turkey
Journal of Lie Theory, Volume 35 (2025) no. 1, pp. 1-16
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.
DOI: 10.5802/jolt.1370
Classification: 17B20,13A50
Keywords: Exponential invariants, character formula

Ahmet Ileri  1 ; Ömer Kücüksakalli  1

1 Dept. of Mathematics, Middle East Technical University, Ankara, Turkey 
Ahmet Ileri; Ömer Kücüksakalli. On the Jacobian Matrices of Generalized Chebyshev Polynomials. Journal of Lie Theory, Volume 35 (2025) no. 1, pp. 1-16. doi: 10.5802/jolt.1370
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