Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VI, Tome 133 (1984), pp. 258-276
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The matrix analogues of the Weierstrass zeta and sigma functions are introduced and studied. It is proved in the case of $\mathbb Z_n\times\mathbb Z_n$ symmetry that the classical $r$-matrix coincides with the matrix zeta function and that the quantum $R$-matrix can be represented as the ratio of matrix sigma functions. The obtained formulae are interpreted as the result of averaging over the lattice in $\mathbb C$.
@article{ZNSL_1984_133_a17,
author = {L. A. Takhtadzhyan},
title = {Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the {Weierstrass} zets and sigma functions},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {258--276},
publisher = {mathdoc},
volume = {133},
year = {1984},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a17/}
}
TY - JOUR AU - L. A. Takhtadzhyan TI - Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions JO - Zapiski Nauchnykh Seminarov POMI PY - 1984 SP - 258 EP - 276 VL - 133 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a17/ LA - ru ID - ZNSL_1984_133_a17 ER -
%0 Journal Article %A L. A. Takhtadzhyan %T Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions %J Zapiski Nauchnykh Seminarov POMI %D 1984 %P 258-276 %V 133 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a17/ %G ru %F ZNSL_1984_133_a17
L. A. Takhtadzhyan. Solutions of the triangle equations with $\mathbb Z_n\times\mathbb Z_n$-symmetry as the matrix analogues of the Weierstrass zets and sigma functions. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VI, Tome 133 (1984), pp. 258-276. http://geodesic.mathdoc.fr/item/ZNSL_1984_133_a17/