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Odd supersymmetrization of elliptic R-matrices
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 is discussed as well. It acquires additional term in the case of supersymmetric R -matrices.
Language:
English
Keywords: elliptic functions
Ustinov A., Математические заметки 2017 Т. 102 № 1 С. 96–108
In the paper, we suggest a method for finding relations concerning series defining the Buchstaber formal group. This method is applied to the cases in which the exponent of the group is an elliptic function of level n=2,3, and 4. An algebraic relation for the series defining the universal Buchstaber formal group is also proved. ...
Added: October 7, 2025
Zabrodin A., Vadim Prokofev, Functional Analysis and Its Applications 2024 Vol. 58 No. 3 P. 289–298
Some identities that involve the elliptic version of the Cauchy matrices are presented
and proved. They include the determinant formula, the formula for the inverse matrix, the matrix
product identity and the factorization formula. ...
Added: November 28, 2024
Prokofiev V., Zabrodin A., Mathematical Physics Analysis and Geometry 2023 Vol. 26 No. 3 Article 20
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By ...
Added: December 4, 2023
Шагай М. А., Флегонтов А. В., В кн.: Некоторые актуальные проблемы современной математики и математического образования. Материалы научной конференции "Герценовские чтения - 2022".: СПб.: РГПУ им. А.И. Герцена, 2022.
This article deals with classes of equations - the Weierstrass orbit, the tangent orbit, and the elliptic integral orbit, - whose solutions have a special structure. Through a finite set of special functions, all solutions are constructed by the method of differential "puzzles" after applying the algorithmic direct method. ...
Added: February 6, 2023
Mosharev P., Кечкин О. В., Moscow University Physics Bulletin 2020 Vol. 75 No. 5 P. 427–433
An exact expression is obtained for harmonic fields in Maxwell electrodynamics with dilatons in terms of elliptic Jacobi functions and elliptic Legendre integrals. The case of centrally symmetric fields is considered individually and effective charges of all three types, that is, electric, magnetic, and dilaton charges, are calculated. An expression is given for the generalized ...
Added: September 28, 2021
A. Levin, M. Olshanetsky, A. Zotov, Journal of Mathematical Physics 2020 Vol. 61 P. 103504
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 odd supersymmetric extensions of the elliptic R-matrices, which satisfy the classical and the associative Yang–Baxter equations. ...
Added: November 10, 2020
Semenov-Tian-Shansky K. M., Поляков М. В., Смирнов А. О. et al., Теоретическая и математическая физика 2019 Т. 200 № 2 С. 290–309
Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear
recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity,
analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group
technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions
of nonlinear recurrence relations relevant for field ...
Added: September 29, 2020
A. Levin, M. Olshanetsky, A. Zotov, / Series arXiv:1910.01814 "math-ph". 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. ...
Added: November 1, 2019
Takebe T., Tokyo: Nippon Hyoron Sha, 2019.
The theory of elliptic integrals and elliptic functions, which were driving force of mathematics in the eighteenth and nineteents centuries, are not only beautiful but have many applications in mathematics and physics. This simple reader-friendly book, based on the lectures at the Faculty of Mathematics, HSE, explains such theory and applications in original way. ...
Added: October 25, 2019
Netay I. V., Mathematical notes 2018 Vol. 103 No. 1-2 P. 232–242
As is well known, the two-parameter Todd genus and the elliptic functions of level d define n-multiplicative Hirzebruch genera if d divides n + 1. Both cases are special cases of the Krichever genera defined by the Baker–Akhiezer function. In the present paper, the inverse problem is solved. Namely, it is proved that only these ...
Added: April 11, 2018