Split Casimir operator and solutions of the Yang–Baxter equation for the $$osp(M|N)$$ and $$s\ell(M|N)$$ Lie superalgebras, higher Casimir operators, and the Vogel parameters

@article{Isaev2022SplitCO,
  title={Split Casimir operator and solutions of the Yang–Baxter equation for the 
 
 
 
 \$\$osp(M|N)\$\$
 and 
 
 
 
 \$\$s\ell(M|N)\$\$
 Lie superalgebras, higher Casimir operators, and the Vogel parameters},
  author={A. P. Isaev and A. A. Provorov},
  journal={Theoretical and Mathematical Physics},
  year={2022},
  volume={210},
  pages={224-260}
}
Abstract We find the characteristic identities for the split Casimir operator in the defining and adjoint representations of the $$osp(M|N)$$ and $$s\ell(M|N)$$ Lie superalgebras. These identities are used to build the projectors onto invariant subspaces of the representation $$T^{\otimes 2}$$ of the $$osp(M|N)$$ and $$s\ell(M|N)$$ Lie superalgebras in the cases where $$T$$ is the defining or adjoint representation. For the defining representation, the $$osp(M|N)$$ - and $$s\ell(M|N… 

References

SHOWING 1-10 OF 37 REFERENCES
Yang-Baxter R-operators for osp superalgebras
Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in defining (minimal fundamental) and adjoint representations. By means of these
Split Casimir Operator and Universal Formulation of the Simple Lie Algebras
TLDR
Characteristic identities for split (polarized) Casimir operators of the simple Lie algebras in adjoint representation are constructed and explicit formulae for invariant projectors onto irreducible subrepresentations in T⊗2 are derived.
Triality, Exceptional Lie Algebras and Deligne Dimension Formulas☆
Abstract We give a computer-free proof of the Deligne, Cohen and de Man formulas for the dimensions of the irreducible g -modules appearing in g ⊗k, k⩽4, where g ranges over the exceptional complex
Introduction to Superanalysis
1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir
Integrable Highest Weight Modules over Affine Superalgebras and Number Theory
The problem of representing an integer as a sum of squares of integers has had a long history. One of the first after antiquity was A. Girard who in 1632 conjectured that an odd prime p can be
Solutions of the Yang-Baxter equation
We give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions. We list the known
Casimir invariants and vector operators in simple and classical Lie algebras
A method of computing eigenvalues of certain types of Casimir invariants has been developed for simple and classical Lie algebras. Especially these eigenvalues for algebrasA n , B n , C n , D n , and
...
...