Journal of Lie Theory 35 (2025), No. 1, 001--016
Copyright Heldermann Verlag 2025
On the Jacobian Matrices of Generalized Chebyshev Polynomials
Ahmet Ileri
Dept. of Mathematics, Middle East Technical University, Ankara, Turkey
ahmet.ileri@metu.edu.tr
Ömer Kücüksakalli
Dept. of Mathematics, Middle East Technical University, Ankara, Turkey
komer@metu.edu.tr
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.
Keywords: Exponential invariants, character formula.
MSC: 17B20,13A50.
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