14 citations · 26 across the 5 of their papers we have counts for
7 papers
Totally positive matrices and dilogarithm identities
Andrei Bytsko, Alexander Volkov
We show that two involutions on the variety of upper triangular totally positive matrices are related, on the one hand, to the tetrahedron equation and, on the other hand,…
Tetrahedron equation, Weyl group, and quantum dilogarithm
Andrei Bytsko, Alexander Volkov
We derive a family of solutions to the tetrahedron equation using the RTT presentation of a two parametric quantized algebra of regular functions on an upper triangular subgroup of…
Tetrahedron equation and cyclic quantum dilogarithm identities
Andrei Bytsko, Alexander Volkov
We establish a hierarchy of quantum dilogarithm identities associated to a sequence of triangular shaped quivers. The tetrahedron equation plays a key role in our construction.
Pentagon Identity Revisited I
Alexander Yu. Volkov
This is to present a previously overlooked q-analog of the five-term dilogarithm relation.
Modeling of Kundu-Eckhaus equation
Dmitry Levko, Alexander Volkov
In work the numerical solutions of Kundu-Eckhaus equation are presented. The conditions of dominate nonlinearity or disperse are cleared up.
From the Tetrahedron Equation to Universal R-Matrices
R. M. Kashaev, A. Yu. Volkov
Modified universal R-matrices, associated with the central extension (through the Drinfeld's double construction) of the quantum groups U_q(sl_n), are realized through an infinite…