Odd supersymmetrization of elliptic R-matrices

@article{Levin2019OddSO,
  title={Odd supersymmetrization of elliptic R-matrices},
  author={Andrei Mikhailovich Levin and Mikhail Aronovich Olshanetsky and A. Zotov},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2019},
  volume={53}
}
We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum elliptic R-matrices. They are shown to satisfy the classical Yang–Baxter equation and the associative Yang–Baxter equation. The quantum Yang–Baxter equation is discussed as well. It acquires additional term in the case of supersymmetric R-matrices. 
View on IOP Publishing
arxiv.org
1 Citations

One Citation

On elliptic solutions of the associative Yang–Baxter equation

References

SHOWING 1-10 OF 50 REFERENCES

Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations

We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct…

Calogero–Moser Model and R-Matrix Identities

We discuss properties of R-matrix-valued Lax pairs for the elliptic Calogero-Moser model. In particular, we show that the family of Hamiltonians arising from this Lax representation contains only…

Quantum Baxter-Belavin R-matrices and multidimensional lax pairs for Painlevé VI

Quantum elliptic R-matrices satisfy the associative Yang-Baxter equation in Mat(N)⊗2, which can be regarded as a noncommutative analogue of the Fay identity for the scalar Kronecker function. We…

Higher-order analogues of the unitarity condition for quantum R-matrices

We derive a family of nth-order identities for quantum R-matrices of the Baxter–Belavin type in the fundamental representation. The set of identities includes the unitarity condition as the simplest…

Classical Yang–Baxter Equation and the A∞-Constraint

Abstract We show that elliptic solutions of classical Yang–Baxter equation (CYBE) can be obtained from triple Massey products on an elliptic curve. We introduce the associative version of this…

UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized…

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…

Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation

In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on the R-matrix description which provides Lax pairs in terms of quantum…

Quadratic Algebras, Dunkl Elements, and Schubert Calculus

We suggest a new combinatorial construction for the cohomology ring of the ag manifold. The degree 2 commutation relations satissed by the divided diierence operators corresponding to positive roots…

Dynamical symmetry of integrable quantum systems