33,234 research outputs found
Higher level WZW sectors from free fermions
We introduce a gauge group of internal symmetries of an ambient algebra as a
new tool for investigating the superselection structure of WZW theories and the
representation theory of the corresponding affine Lie algebras. The relevant
ambient algebra arises from the description of these conformal field theories
in terms of free fermions. As an illustration we analyze in detail the \son\
WZW theories at level two. In this case there is actually a homomorphism from
the representation ring of the gauge group to the WZW fusion ring, even though
the level-two observable algebra is smaller than the gauge invariant subalgebra
of the field algebra.Comment: LaTeX2e, 30 page
Multiparameter quantum groups at roots of unity
We address the problem of studying multiparameter quamtum groups (=MpQG's) at
roots of unity, namely quantum universal enveloping algebras depending on a matrix of parameters . This is performed
via the construction of quantum root vectors and suitable "integral forms" of , a restricted one - generated by
quantum divided powers and quantum binomial coefficients - and an unrestricted
one - where quantum root vectors are suitably renormalized. The specializations
at roots of unity of either forms are the "MpQG's at roots of unity" we are
investigating. In particular, we study special subalgebras and quotients of our
MpQG's at roots of unity - namely, the multiparameter version of small quantum
groups - and suitable associated quantum Frobenius morphisms, that link the
(specializations of) MpQG's at roots of 1 with MpQG's at 1, the latter being
classical Hopf algebras bearing a well precise Poisson-geometrical content. A
key point in the discussion - often at the core of our strategy - is that every
MpQG is actually a 2-cocycle deformation of the algebra structure of (a lift
of) the "canonical" one-parameter quantum group by Jimbo-Lusztig, so that we
can often rely on already established results available for the latter. On the
other hand, depending on the chosen multiparameter our
quantum groups yield (through the choice of integral forms and their
specialization) different semiclassical structures, namely different Lie
coalgebra structures and Poisson structures on the Lie algebra and algebraic
group underlying the canonical one-parameter quantum group.Comment: 84 pages. New version slightly re-edited and streamlined: the content
only is affected in Sec. 3.1, but page flushing occurs in the sequel as well
(overall, the text is now one page shorter
Lie-Algebraic Characterization of 2D (Super-)Integrable Models
It is pointed out that affine Lie algebras appear to be the natural
mathematical structure underlying the notion of integrability for
two-dimensional systems. Their role in the construction and classification of
2D integrable systems is discussed. The super- symmetric case will be
particularly enphasized. The fundamental examples will be outlined.Comment: 6 pages, LaTex, Talk given at the conference in memory of D.V.
Volkov, Kharkhov, January 1997. To appear in the proceeding
Higher-dimensional WZW Model on K\"ahler Manifold and Toroidal Lie Algebra
We construct a generalization of the two-dimensional Wess-Zumino-Witten model
on a -dimensional K\"ahler manifold as a group-valued non-linear sigma
model with an anomaly term containing the K\"ahler form. The model is shown to
have an infinite-dimensional symmetry which generates an -toroidal Lie
algebra. The classical equation of motion turns out to be the
Donaldson-Uhlenbeck-Yau equation, which is a -dimensional generalization of
the self-dual Yang-Mills equation.Comment: 12 pages, Late
The gl(M|N) Super Yangian and Its Finite Dimensional Representations
Methods are developed for systematically constructing the finite dimensional
irreducible representations of the super Yangian Y(gl(M|N)) associated with the
Lie superalgebra gl(M|N). It is also shown that every finite dimensional
irreducible representation of Y(gl(M|N)) is of highest weight type, and is
uniquely characterized by a highest weight. The necessary and sufficient
conditions for an irrep to be finite dimensional are given.Comment: 14 pages plain late
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