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Статья

Isaev, A.P.
Split Casimir Operator for Simple Lie Algebras in the Cube of ad-Representation and Vogel Parameters / A.P.Isaev, S.O.Krivonos, A.A.Provorov // International Journal of Modern Physics A [Electronic resource]. – 2023. – Vol.38, No.6/7. – P.2350037. – URL: https://doi.org/10.1142/S0217751X23500379. – Bibliogr.:23.

In this paper, we constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations ad and deduced a certain class of subrepresentations in ad⊗3. The projectors onto invariant subspaces for these subrepresentations were directly constructed from the characteristic identities for the 3-split Casimir operators. For all simple Lie algebras, universal expressions for the traces of higher powers of the 3-split Casimir operators were found and dimensions of the subrepresentations in ad⊗3 were calculated. All our formulas are in agreement with the universal description of (irreducible) subrepresentations in ad⊗3 for simple Lie algebras in terms of the Vogel parameters.



ОИЯИ = ОИЯИ (JINR)2023
Спец.(статьи,препринты) = С 323 б - Квантовые алгебры. Суперсимметричная квантовая механика. Парастатистики . Анионы. Прочие схемы квантования
Спец.(статьи,препринты) = С 323.5 - Теория взаимодействия частиц при высоких энергиях$
Бюллетени = 4/024