3,227 research outputs found
Ramond sector of superconformal algebras via quantum reduction
Quantum hamiltonian reduction of affine superalgebras is studied in the
twisted case. The Ramond sector of "minimal" superconformal W-algebras is
described in detail, the determinant formula is obtained. Extensive list of
examples includes all the simple Lie superalgebras of rank up to 2. The paper
generalizes the results of Kac and Wakimoto (math-ph/0304011) to the twisted
case.Comment: 50 pages, 8 figures; v2: examples added, determinant formula
derivation modified, section order change
Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction
We note that a version ``with spectral parameter'' of the Drinfeld-Sokolov
reduction gives a natural mapping from the KdV phase space to the group of
loops with values in ~: affine nilpotent and
principal commutative (or anisotropic Cartan) subgroup~; this mapping is
connected to the conserved densities of the hierarchy. We compute the
Feigin-Frenkel action of (defined in terms of screening
operators) on the conserved densities, in the case
Fusion and singular vectors in A1{(1)} highest weight cyclic modules
We show how the interplay between the fusion formalism of conformal field
theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for
the singular vectors in the highest weight representations of A1{(1)}.Comment: 42 page
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
On the forward-backward charge asymmetry in e+e- -annihilation into hadrons at high energies
The forward-backward asymmetry in e+ e- annihilation into a quark-antiquark
pair is considered in the double-logarithmic approximation at energies much
higher than the masses of the weak bosons. It is shown that after accounting to
all orders for the exchange of virtual photons and W, Z -bosons one is lead to
the following effect (asymmetry): quarks with positive electric charge (e.g. u,
\bar{d}) tend to move in the e+ - direction whereas quarks with negative
charges (e.g. d, \bar{u}) tend to move in the e- - direction. The value of the
asymmetry grows with increasing energy when the produced quarks are within a
cone with opening angle, in the cmf, \theta_0\sim 2M_Z/\sqrt{s} around the e+e-
-beam. Outside this cone, at \theta_0 << \theta << 1, the asymmetry is
inversely proportional to \theta .Comment: 17 Pages, 2 Tables, 4 Figures. Hadronization effects to the asymmetry
are considered with more detail
Quantum R-matrix and Intertwiners for the Kashiwara Algebra
We study the algebra presented by Kashiwara and introduce
intertwiners similar to -vertex operators. We show that a matrix determined
by 2-point functions of the intertwiners coincides with a quantum R-matrix (up
to a diagonal matrix) and give the commutation relations of the intertwiners.
We also introduce an analogue of the universal R-matrix for the Kashiwara
algebra.Comment: 21 page
The puzzle of 90 degree reorientation in the vortex lattice of borocarbide superconductors
We explain 90 degree reorientation in the vortex lattice of borocarbide
superconductors on the basis of a phenomenological extension of the nonlocal
London model that takes full account of the symmetry of the system. We propose
microscopic mechanisms that could generate the correction terms and point out
the important role of the superconducting gap anisotropy.Comment: 4 pages, 2 eps figure
Supersymmetric vertex algebras
We define and study the structure of SUSY Lie conformal and vertex algebras.
This leads to effective rules for computations with superfields.Comment: 71 page
W_{1+\infty} and W(gl_N) with central charge N
We study representations of the central extension of the Lie algebra of
differential operators on the circle, the W-infinity algebra. We obtain
complete and specialized character formulas for a large class of
representations, which we call primitive; these include all quasi-finite
irreducible unitary representations. We show that any primitive representation
with central charge N has a canonical structure of an irreducible
representation of the W-algebra W(gl_N) with the same central charge and that
all irreducible representations of W(gl_N) with central charge N arise in this
way. We also establish a duality between "integral" modules of W(gl_N) and
finite-dimensional irreducible modules of gl_N, and conjecture their fusion
rules.Comment: 29 pages, Latex, uses file amssym.def (a few remarks added, typos
corrected
More on quantum groups from the the quantization point of view
Star products on the classical double group of a simple Lie group and on
corresponding symplectic grupoids are given so that the quantum double and the
"quantized tangent bundle" are obtained in the deformation description.
"Complex" quantum groups and bicovariant quantum Lie algebras are discused from
this point of view. Further we discuss the quantization of the Poisson
structure on symmetric algebra leading to the quantized enveloping
algebra as an example of biquantization in the sense of Turaev.
Description of in terms of the generators of the bicovariant
differential calculus on is very convenient for this purpose. Finally
we interpret in the deformation framework some well known properties of compact
quantum groups as simple consequences of corresponding properties of classical
compact Lie groups. An analogue of the classical Kirillov's universal character
formula is given for the unitary irreducible representation in the compact
case.Comment: 18 page
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