On the Jacobian Matrices of Generalized Chebyshev Polynomials

Key Points

• The aim is to develop a method for calculating Jacobian matrices of generalized Chebyshev polynomials connected to semisimple Lie algebras.
• Develop a practical computation method for Jacobian matrices.
• Express matrix entries as linear combinations of characters of irreducible representations.
• Utilize integer coefficients derived through calculations in the fundamental Weyl chamber.
• Jacobian matrix entries are successfully computed as combinations of irreducible representations.
• Integer coefficients corresponding to the entries are obtained with basic computations.
• The method enhances understanding of the properties of generalized Chebyshev polynomials in Lie algebras.