On the Jacobian Matrices of Generalized Chebyshev Polynomials

OpenAlex İngilizce

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.