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.
Classification :
17B20,13A50
Mots-clés :
Exponential invariants, character formula
Affiliations des auteurs :
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, Tome 35 (2025) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/JOLT_2025_35_1_a0/
@article{JOLT_2025_35_1_a0,
author = {Ahmet Ileri and \"Omer 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_1_a0/}
}
TY - JOUR
AU - Ahmet Ileri
AU - Ömer 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 - http://geodesic.mathdoc.fr/item/JOLT_2025_35_1_a0/
ID - JOLT_2025_35_1_a0
ER -
%0 Journal Article
%A Ahmet Ileri
%A Ömer 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 http://geodesic.mathdoc.fr/item/JOLT_2025_35_1_a0/
%F JOLT_2025_35_1_a0
