193 research outputs found
Representations of affine Lie algebras, elliptic r-matrix systems, and special functions
There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8,
6.11. These errors have been corrected in the present version of this paper.
There are also some minor changes in the introduction.Comment: 33 pages, no figure
Multiinstantons in curvilinear coordinates
The 'tHooft's 5N-parametric multiinstanton solution is generalized to
curvilinear coordinates. Expressions can be simplified by a gauge
transformation that makes -symbols constant in the vierbein formalism.
This generates the compensating addition to the gauge potential of
pseudoparticles. Typical examples (4-spherical, 2+2- and 3+1-cylindrical
coordinates) are studied and explicit formulae presented for reference.
Singularities of the compensating field are discussed. They are irrelevant for
physics but affect gauge dependent quantities.Comment: LaTeX file, 17 page
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
We study classical twists of Lie bialgebra structures on the polynomial
current algebra , where is a simple complex
finite-dimensional Lie algebra. We focus on the structures induced by the
so-called quasi-trigonometric solutions of the classical Yang-Baxter equation.
It turns out that quasi-trigonometric -matrices fall into classes labelled
by the vertices of the extended Dynkin diagram of . We give
complete classification of quasi-trigonometric -matrices belonging to
multiplicity free simple roots (which have coefficient 1 in the decomposition
of the maximal root). We quantize solutions corresponding to the first root of
.Comment: 41 pages, LATE
On the Fermionic Quasi-particle Interpretation in Minimal Models of Conformal Field Theory
The conjecture that the states of the fermionic quasi-particles in minimal
conformal field theories are eigenstates of the integrals of motion to certain
eigenvalues is checked and shown to be correct only for the Ising model.Comment: 5 pages of Late
How to find discrete contact symmetries
This paper describes a new algorithm for determining all discrete contact
symmetries of any differential equation whose Lie contact symmetries are known.
The method is constructive and is easy to use. It is based upon the observation
that the adjoint action of any contact symmetry is an automorphism of the Lie
algebra of generators of Lie contact symmetries. Consequently, all contact
symmetries satisfy various compatibility conditions. These conditions enable
the discrete symmetries to be found systematically, with little effort
On the Classification of Automorphic Lie Algebras
It is shown that the problem of reduction can be formulated in a uniform way
using the theory of invariants. This provides a powerful tool of analysis and
it opens the road to new applications of these algebras, beyond the context of
integrable systems. Moreover, it is proven that sl2-Automorphic Lie Algebras
associated to the icosahedral group I, the octahedral group O, the tetrahedral
group T, and the dihedral group Dn are isomorphic. The proof is based on
techniques from classical invariant theory and makes use of Clebsch-Gordan
decomposition and transvectants, Molien functions and the trace-form. This
result provides a complete classification of sl2-Automorphic Lie Algebras
associated to finite groups when the group representations are chosen to be the
same and it is a crucial step towards the complete classification of
Automorphic Lie Algebras.Comment: 29 pages, 1 diagram, 9 tables, standard LaTeX2e, submitted for
publicatio
Two-Dimensional Critical Percolation: The Full Scaling Limit
We use SLE(6) paths to construct a process of continuum nonsimple loops in
the plane and prove that this process coincides with the full continuum scaling
limit of 2D critical site percolation on the triangular lattice -- that is, the
scaling limit of the set of all interfaces between different clusters. Some
properties of the loop process, including conformal invariance, are also
proved.Comment: 45 pages, 12 figures. This is a revised version of math.PR/0504036
without the appendice
From Zwiebach invariants to Getzler relation
We introduce the notion of Zwiebach invariants that generalize Gromov-Witten
invariants and homotopical algebra structures. We outline the induction
procedure that induces the structure of Zwiebach on the subbicomplex, that
gives the structure of Gromov-Witten invariants on subbicomplex with zero
diffferentials. We propose to treat Hodge dGBV with 1/12 axiom as the simplest
set of Zwiebach invariants, and explicitely prove that it induces WDVV and
Getzler equations in genera 0 and 1 respectively.Comment: 35 page
On the Structure of the Fusion Ideal
We prove that there is a finite level-independent bound on the number of
relations defining the fusion ring of positive energy representations of the
loop group of a simple, simply connected Lie group. As an illustration, we
compute the fusion ring of at all levels
Vertex--IRF correspondence and factorized L-operators for an elliptic R-operator
As for an elliptic -operator which satisfies the Yang--Baxter equation,
the incoming and outgoing intertwining vectors are constructed, and the
vertex--IRF correspondence for the elliptic -operator is obtained. The
vertex--IRF correspondence implies that the Boltzmann weights of the IRF model
satisfy the star--triangle relation. By means of these intertwining vectors,
the factorized L-operators for the elliptic -operator are also constructed.
The vertex--IRF correspondence and the factorized L-operators for Belavin's
-matrix are reproduced from those of the elliptic -operator.Comment: 25 pages, amslatex, no figure
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