245 research outputs found
On the Kontsevich integral for knotted trivalent graphs
We construct an extension of the Kontsevich integral of knots to knotted
trivalent graphs, which commutes with orientation switches, edge deletions,
edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first
constructed such an extension, building on Drinfel'd's theory of associators.
We construct a step by step definition, using elementary Kontsevich integral
methods, to get a one-parameter family of corrections that all yield invariants
well behaved under the graph operations above.Comment: Journal version, 47 page
Asymptotic representations and Drinfeld rational fractions
We introduce and study a category of representations of the Borel algebra,
associated with a quantum loop algebra of non-twisted type. We construct
fundamental representations for this category as a limit of the
Kirillov-Reshetikhin modules over the quantum loop algebra and we establish
explicit formulas for their characters. We prove that general simple modules in
this category are classified by n-tuples of rational functions in one variable,
which are regular and non-zero at the origin but may have a zero or a pole at
infinity.Comment: 32 pages; accepted for publication in Compositio Mathematic
(Non)renormalizability of the D-deformed Wess-Zumino model
We continue the analysis of the -deformed Wess-Zumino model which was
started in the previous paper. The model is defined by a deformation which is
non-hermitian and given in terms of the covariant derivatives . We
calculate one-loop divergences in the two-point, three-point and four-point
Green functions. We find that the divergences in the four-point function cannot
be absorbed and thus our model is not renormalizable. We discuss possibilities
to render the model renormalizable.Comment: 19 pages; version accepted for publication in Phys.Rev.D; new section
with the detailed discussion on renormalizabilty added and a special choice
of coupling constants which renders the model renormalizable analyze
Twisted Yangians and folded W-algebras
We show that the truncation of twisted Yangians are isomorphic to finite
W-algebras based on orthogonal or symplectic algebras. This isomorphism allows
us to classify all the finite dimensional irreducible representations of the
quoted W-algebras. We also give an R-matrix for these W-algebras, and determine
their center.Comment: LaTeX 2e Document, 22 page
Kummer Theory for Drinfeld Modules
Let {\phi} be a Drinfeld A-module of characteristic p0 over a finitely
generated field K. Previous articles determined the image of the absolute
Galois group of K up to commensurability in its action on all prime-to-p0
torsion points of {\phi}, or equivalently, on the prime-to-p0 adelic Tate
module of {\phi}. In this article we consider in addition a finitely generated
torsion free A-submodule M of K for the action of A through {\phi}. We
determine the image of the absolute Galois group of K up to commensurability in
its action on the prime-to-p0 division hull of M, or equivalently, on the
extended prime-to-p0 adelic Tate module associated to {\phi} and M
Twisted Yangians of small rank
We study quantized enveloping algebras called twisted Yangians associated with the symmetric pairs of types CI, BDI, and DIII (in Cartan’s classification) when the rank is small. We establish isomorphisms between these twisted Yangians and the well known Olshanskii’s twisted Yangians of types AI and AII, and also with the Molev-Ragoucy reflection algebras associated with symmetric pairs of type AIII. We also construct isomorphisms with twisted Yangians in Drinfeld’s original presentation
Coadjoint Poisson actions of Poisson-Lie groups
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie
algebra induces on it a non-trivial class of quadratic Poisson structures
extending the linear Poisson bracket on the coadjoint orbits
Twisted K-Theory for the Orbifold [*/G]
We study the relationship between the twisted Orbifold K-theories
{^{\alpha}}K_{orb}(\textsl{X}) and {^{\alpha'}}K_{orb}(\textsl{Y}) for two
different twists and of the
Orbifolds \textsl{X}=[*/G] and \textsl{Y}=[*/G'] respectively, for and
finite groups. We prove that under suitable hypothesis over the twisting
and the group we obtain an isomorphism between these twisted
K-theories.Comment: version accepted in Pacific Journal of Mathematic
Lie-Poisson Deformation of the Poincar\'e Algebra
We find a one parameter family of quadratic Poisson structures on which satisfies the property {\it a)} that it is preserved
under the Lie-Poisson action of the Lorentz group, as well as {\it b)} that it
reduces to the standard Poincar\'e algebra for a particular limiting value of
the parameter. (The Lie-Poisson transformations reduce to canonical ones in
that limit, which we therefore refer to as the `canonical limit'.) Like with
the Poincar\'e algebra, our deformed Poincar\'e algebra has two Casimir
functions which we associate with `mass' and `spin'. We parametrize the
symplectic leaves of with space-time coordinates,
momenta and spin, thereby obtaining realizations of the deformed algebra for
the cases of a spinless and a spinning particle. The formalism can be applied
for finding a one parameter family of canonically inequivalent descriptions of
the photon.Comment: Latex file, 26 page
Integration of twisted Poisson structures
Poisson manifolds may be regarded as the infinitesimal form of symplectic
groupoids. Twisted Poisson manifolds considered by Severa and Weinstein
[math.SG/0107133] are a natural generalization of the former which also arises
in string theory. In this note it is proved that twisted Poisson manifolds are
in bijection with a (possibly singular) twisted version of symplectic
groupoids.Comment: 12 pages; minor corrections (especially in terminology: "twisted
symplectic" replaces "quasi-symplectic"), references updated; to appear in J.
Geom. Phy
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