793 research outputs found
Tetrahedron Reflection Equation
Reflection equation for the scattering of lines moving in half-plane is
obtained. The corresponding geometric picture is related with configurations of
half-planes touching the boundary plane in 2+1 dimensions. This equation can be
obtained as an additional to the tetrahedron equation consistency condition for
a modified Zamolodchikov algebra.Comment: 10 pages, LaTe
Twist Deformation of the rank one Lie Superalgebra
The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie
superalgebra . The twist element is the same as for the Lie
algebra due to the embedding of the into the superalgebra .
The R-matrix has the direct sum structure in the irreducible representations of
. The dual quantum group is defined using the FRT-formalism. It
includes the Jordanian quantum group as subalgebra and Grassmann
generators as well.Comment: LaTeX, 9 page
Deformation of orthosymplectic Lie superalgebra osp(1|2)
Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is
defined by chains of twists. Corresponding classical r-matrix is obtained by a
contraction procedure from the trigonometric r-matrix. The carrier space of the
constant r-matrix is the Borel subalgebra.Comment: LaTeX, 8 page
Quantization of the N=2 Supersymmetric KdV Hierarchy
We continue the study of the quantization of supersymmetric integrable KdV
hierarchies. We consider the N=2 KdV model based on the affine
algebra but with a new algebraic construction for the L-operator, different
from the standard Drinfeld-Sokolov reduction. We construct the quantum
monodromy matrix satisfying a special version of the reflection equation and
show that in the classical limit, this object gives the monodromy matrix of N=2
supersymmetric KdV system. We also show that at both the classical and the
quantum levels, the trace of the monodromy matrix (transfer matrix) is
invariant under two supersymmetry transformations and the zero mode of the
associated U(1) current.Comment: LaTeX2e, 12 page
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