136 research outputs found
On the R-matrix realization of Yangians and their representations
We study the Yangians Y(a) associated with the simple Lie algebras a of type
B, C or D. The algebra Y(a) can be regarded as a quotient of the extended
Yangian X(a) whose defining relations are written in an R-matrix form. In this
paper we are concerned with the algebraic structure and representations of the
algebra X(a). We prove an analog of the Poincare-Birkhoff-Witt theorem for X(a)
and show that the Yangian Y(a) can be realized as a subalgebra of X(a).
Furthermore, we give an independent proof of the classification theorem for the
finite-dimensional irreducible representations of X(a) which implies the
corresponding theorem of Drinfeld for the Yangians Y(a). We also give explicit
constructions for all fundamental representation of the Yangians.Comment: 65 page
Determinant representations for form factors in quantum integrable models with GL(3)-invariant R-matrix
We obtain determinant representations for the form factors of the monodromy
matrix entries in quantum integrable models solvable by the nested algebraic
Bethe ansatz and possessing -invariant -matrix. These representations
can be used for the calculation of correlation functions in the models of
physical interest.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1312.148
Scalar products in models with trigonometric -matrix. General case
We study quantum integrable models with trigonometric -matrix
solvable by the nested algebraic Bethe ansatz. We analyze scalar products of
generic Bethe vectors and obtain an explicit representation for them in terms
of a sum with respect to partitions of Bethe parameters. This representation
generalizes known formula for the scalar products in the models with
-invariant -matrix.Comment: 23 page
Form factors of local operators in a one-dimensional two-component Bose gas
We consider a one-dimensional model of a two-component Bose gas and study
form factors of local operators in this model. For this aim we use an approach
based on the algebraic Bethe ansatz. We show that the form factors under
consideration can be reduced to those of the monodromy matrix entries in a
generalized GL(3)-invariant model. In this way we derive determinant
representations for the form factors of local operators.Comment: 23 pages. arXiv admin note: text overlap with arXiv:1502.0196
Segal-Sugawara vectors for the Lie algebra of type
Explicit formulas for Segal-Sugawara vectors associated with the simple Lie
algebra of type are found by using computer-assisted
calculations. This leads to a direct proof of the Feigin-Frenkel theorem
describing the center of the corresponding affine vertex algebra at the
critical level. As an application, we give an explicit solution of Vinberg's
quantization problem by providing formulas for generators of maximal
commutative subalgebras of . We also calculate the eigenvalues
of the Hamiltonians on the Bethe vectors in the Gaudin model associated with
.Comment: 26 page
Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient
We study quantum integrable models with GL(3) trigonometric R-matrix solvable
by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such
models can be expressed in terms of a bilinear combination of the highest
coefficients. We show that in the models with GL(3) trigonometric R-matrix
there exist two different highest coefficients. We obtain various
representations for them in terms of sums over partitions. We also prove
several important properties of the highest coefficients, which are necessary
for the evaluation of the scalar products.Comment: 27 page
Form factors in quantum integrable models with GL(3)-invariant R-matrix
We study integrable models solvable by the nested algebraic Bethe ansatz and
possessing GL(3)-invariant R-matrix. We obtain determinant representations for
form factors of off-diagonal entries of the monodromy matrix. These
representations can be used for the calculation of form factors and correlation
functions of the XXX SU(3)-invariant Heisenberg chain.Comment: 27 pages; typos correcte
Form factors in SU(3)-invariant integrable models
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe
ansatz. We obtain determinant representations for form factors of diagonal
entries of the monodromy matrix. This representation can be used for the
calculation of form factors and correlation functions of the XXX
SU(3)-invariant Heisenberg chain.Comment: 15 pages; typos correcte
Bethe vectors of GL(3)-invariant integrable models
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe
ansatz. Different formulas are given for the Bethe vectors and the actions of
the generators of the Yangian Y(sl(3)) on Bethe vectors are considered. These
actions are relevant for the calculation of correlation functions and form
factors of local operators of the underlying quantum models.Comment: 22 pages, typos correcte
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