Journal of Lie Theory

no. 1
On the Jacobian Matrices of Generalized Chebyshev Polynomials
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 
@article{JOLT_2025_35_1_a0,
     author = {A. Ileri and \"O. K\"uc\"uksakalli},
     title = {On the {Jacobian} {Matrices} of {Generalized} {Chebyshev} {Polynomials}},
     journal = {Journal of Lie Theory},
     pages = {1--16},
     year = {2025},
     volume = {35},
     number = {1},
     doi = {10.5802/jolt.1370},
     zbl = {1562.17020},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1370/}
}
TY  - JOUR
AU  - A. Ileri
AU  - Ö. Kücüksakalli
TI  - On the Jacobian Matrices of Generalized Chebyshev Polynomials
JO  - Journal of Lie Theory
PY  - 2025
SP  - 1
EP  - 16
VL  - 35
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1370/
DO  - 10.5802/jolt.1370
ID  - JOLT_2025_35_1_a0
ER  - 
%0 Journal Article
%A A. Ileri
%A Ö. Kücüksakalli
%T On the Jacobian Matrices of Generalized Chebyshev Polynomials
%J Journal of Lie Theory
%D 2025
%P 1-16
%V 35
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1370/
%R 10.5802/jolt.1370
%F JOLT_2025_35_1_a0
A. Ileri; Ö. 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

Cited by Sources: