79 citations · 807 across the 61 of their papers we have counts for
16 papers · 1 filter
Split Casimir operator for simple Lie algebras in the cube of -representation and Vogel parameters
A. P. Isaev, S. O. Krivonos, A. A. Provorov
We constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations and deduced a certain cla…
Flat connection on four-dimensional lattice, related matrix difference equations and their solutions
H. Boos, A. P. Isaev
In the paper [H.Boos, A.Hutsalyuk and Kh.Nirov, J.Phys.A:Math.Theor. 51 (2018) 445202] the reduced density matrix of the sl(3)-invariant fundamental exchange model was calculated f…
The split Casimir operator and solutions of the Yang-Baxter equation for the and Lie superalgebras, higher Casimir operators, and the Vogel parameters
A. P. Isaev, A. A. Provorov
We find the characteristic identities for the split Casimir operator in the defining and adjoint representations of the and Lie superalgebras. These identit…
Split Casimir operator and universal formulation of the simple Lie algebras
A. P. Isaev, S. O. Krivonos
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities…
Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations and Vogel parameters
A. P. Isaev, S. O. Krivonos
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in defining (minimal fundamental) and adjoint representations. By mean…
Projectors on invariant subspaces of representations of Lie algebras and and Vogel parametrization
A. P. Isaev, A. A. Provorov
Explicit formulae for the projectors onto invariant subspaces of the representation of the Lie algebras and have been found by mean…
Yang-Baxter R-operators for osp superalgebras
A. P. Isaev, D. Karakhanyan, R. Kirschner
We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic -operators with orthogon…
Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras
J. Fuksa, A. P. Isaev, D. Karakhanyan +1
Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start from the formulation of graded algebras and the linear superspace carrying…
Orthogonal and symplectic Yangians and Yang-Baxter R-operators
A. P. Isaev, D. Karakhanyan, R. Kirschner
Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operat…
Remarks towards the spectrum of the Heisenberg spin chain type models
C. Burdik, J. Fuksa, A. P. Isaev +2
The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX…
Spinorial R-matrix
D. Chicherin, S. Derkachov, A. P. Isaev
R-matrix acting in the tensor product of two spinor representation spaces of Lie algebra so(d) is considered thoroughly. Corresponding Yang-Baxter equation is proved. The relation…
Conformal algebra: R-matrix and star-triangle relation
D. Chicherin, S. Derkachov, A. P. Isaev
The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solve…
Functional equations for transfer-matrix operators in open Hecke chain models
A. P. Isaev
We consider integrable open chain models formulated in terms of generators of affine Hecke algebras. The hierarchy of commutative elements (which are analogs of the commutative tra…
BRST charges for finite nonlinear algebras
A. P. Isaev, S. O. Krivonos, O. V. Ogievetsky
Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie alg…
BRST operators for W algebras
A. P. Isaev, S. O. Krivonos, O. V. Ogievetsky
The study of quantum Lie algebras motivates a use of non-canonical ghosts and anti-ghosts for non-linear algebras, like W-algebras. This leads, for the W_3 and W_3^(2) algebras, to…
Baxterized Solutions of Reflection Equation and Integrable Chain Models
A. P. Isaev, O. V. Ogievetsky
Non-polynomial Baxterized solutions of reflection equations associated with affine Hecke and affine Birman-Murakami-Wenzl algebras are found. Relations to integrable spin chain mod…