On the Jacobian Matrices of Generalized Chebyshev Polynomials

İleri A., KÜÇÜKSAKALLI Ö.

Journal of Lie Theory, cilt.35, sa.1, ss.1-16, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 1
  • Basım Tarihi: 2025
  • Dergi Adı: Journal of Lie Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1-16
  • Anahtar Kelimeler: character formula, Exponential invariants
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.