# Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations

@article{Levin2019OddSK, title={Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations}, author={Andrei Mikhailovich Levin and Mikhail Aronovich Olshanetsky and A. Zotov}, journal={arXiv: Mathematical Physics}, year={2019} }

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 an odd supersymmetric extensions of the elliptic $R$-matrices, which satisfy the classical and the associative Yang-Baxter equations.

## One Citation

### Odd supersymmetrization of elliptic R-matrices

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

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…

## References

SHOWING 1-10 OF 26 REFERENCES

### On Some Quadratic Algebras I 1/2: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials

- Mathematics
- 2016

We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of…

### Notes on super Riemann surfaces and their moduli

- MathematicsPure and Applied Mathematics Quarterly
- 2019

These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS…

### Theta Functions on Riemann Surfaces

- Mathematics
- 1973

Riemann's theta function.- The prime-form.- Degenerate Riemann surfaces.- Cyclic unramified coverings.- Ramified double coverings.- Bordered Riemann surfaces.

### Planck constant as spectral parameter in integrable systems and KZB equations

- Mathematics
- 2014

A bstractWe construct special rational glN Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum glN rational R-matrix. They have two parameters.…

### Calogero–Moser Model and R-Matrix Identities

- MathematicsTheoretical and Mathematical Physics
- 2018

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…

### Solutions of the Yang-Baxter equation

- Mathematics
- 1982

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…