73 research outputs found
Perturbative BPS-algebras in superstring theory
This paper investigates the algebraic structure that exists on perturbative
BPS-states in the superstring, compactified on the product of a circle and a
Calabi-Yau fourfold. This structure was defined in a recent article by Harvey
and Moore. It shown that for a toroidal compactification this algebra is
related to a generalized Kac-Moody algebra. The BPS-algebra itself is not a
Lie-algebra. However, it turns out to be possible to construct a Lie-algebra
with the same graded dimensions, in terms of a half-twisted model. The
dimensions of these algebras are related to the elliptic genus of the
transverse part of the string algebra. Finally, the construction is applied to
an orbifold compactification of the superstring.Comment: 31 pages, latex, no figure
KdV type hierarchies, the string equation and constraints
To every partition one can associate a vertex operator
realization of the Lie algebras and . Using this
construction we make reductions of the --component KP hierarchy, reductions
which are related to these partitions. In this way we obtain matrix KdV type
equations. Now assuming that (1) is a --function of the
--th reduced KP hierarchy and (2) satisfies a
`natural' string equation, we prove that also satisfies the vacuum
constraints of the algebra.Comment: 29 pages of amstex, Correction of some errors and 1 reference adde
Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies
Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade
one regular semisimple elements from non-equivalent Heisenberg subalgebras of a
loop algebra \G\otimes{\bf C}[\lambda,\lambda^{-1}] are studied. The graded
Heisenberg subalgebras containing such elements are labelled by the regular
conjugacy classes in the Weyl group {\bf W}(\G) of the simple Lie algebra
\G. A representative w\in {\bf W}(\G) of a regular conjugacy class can be
lifted to an inner automorphism of \G given by , where is the defining vector of an subalgebra
of \G.The grading is then defined by the operator and any grade one regular element from the
Heisenberg subalgebra associated to takes the form , where and is included in an
subalgebra containing . The largest eigenvalue of is
except for some cases in , . We explain how these Lie
algebraic results follow from known results and apply them to construct
integrable systems.If the largest eigenvalue is , then
using any grade one regular element from the Heisenberg subalgebra associated
to we can construct a KdV system possessing the standard \W-algebra
defined by as its second Poisson bracket algebra. For \G a classical
Lie algebra, we derive pseudo-differential Lax operators for those
non-principal KdV systems that can be obtained as discrete reductions of KdV
systems related to . Non-abelian Toda systems are also considered.Comment: 44 pages, ENSLAPP-L-493/94, substantial revision, SWAT-95-77. (use
OLATEX (preferred) or LATEX
Similarity reduction of the modified Yajima-Oikawa equation
We study a similarity reduction of the modified Yajima-Oikawa hierarchy. The
hierarchy is associated with a non-standard Heisenberg subalgebra in the affine
Lie algebra of type A_2^{(1)}. The system of equations for self-similar
solutions is presented as a Hamiltonian system of degree of freedom two, and
admits a group of B\"acklund transformations isomorphic to the affine Weyl
group of type A_2^{(1)}. We show that the system is equivalent to a
two-parameter family of the fifth Painlev\'e equation.Comment: latex2e file, 18 pages, no figures; (v2)Introduction is modified.
Some typos are correcte
Afscheid van de klassieke procedure? Een verslag van een afscheid en een weerzien
Criminal Justice: Legitimacy, accountability, and effectivit
Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves
We define complexes of vector bundles on products of moduli spaces of framed
rank r torsion-free sheaves on the complex projective plane. The top
non-vanishing Chern classes of the cohomology of these complexes yield actions
of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology
of the moduli spaces. In this way we obtain a geometric realization of the
boson-fermion correspondence and related vertex operators.Comment: 36 pages; v2: Definition of geometric Heisenberg operators modified;
v3: Minor typos correcte
Dressing Technique for Intermediate Hierarchies
A generalized AKNS systems introduced and discussed recently in \cite{dGHM}
are considered. It was shown that the dressing technique both in matrix
pseudo-differential operators and formal series with respect to the spectral
parameter can be developed for these hierarchies.Comment: 16 pages, LaTeX Report/no: DFTUZ/94/2
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local
reductions of Hamiltonian flows generated by monodromy invariants on the dual
of a loop algebra. Following earlier work of De Groot et al, reductions based
upon graded regular elements of arbitrary Heisenberg subalgebras are
considered. We show that, in the case of the nontwisted loop algebra
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case considered by DS. The methods of DS are
utilized throughout the analysis, but formulating the reduction entirely within
the Hamiltonian framework provided by the classical r-matrix approach leads to
some simplifications even for .Comment: 43 page
On Separation of Variables for Integrable Equations of Soliton Type
We propose a general scheme for separation of variables in the integrable
Hamiltonian systems on orbits of the loop algebra
. In
particular, we illustrate the scheme by application to modified Korteweg--de
Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg
magnetic equations.Comment: 22 page
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