2,088 research outputs found
On multigraded generalizations of Kirillov-Reshetikhin modules
We study the category of Z^l-graded modules with finite-dimensional graded
pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre
subcategories with finitely many isomorphism classes of simple objects. We
construct projective resolutions for the simple modules in these categories and
compute the Ext groups between simple modules. We show that the projective
covers of the simple modules in these Serre subcategories can be regarded as
multigraded generalizations of Kirillov-Reshetikhin modules and give a
recursive formula for computing their graded characters
Extended T-systems
We use the theory of q-characters to establish a number of short exact
sequences in the category of finite-dimensional representations of the quantum
affine groups of types A and B. That allows us to introduce a set of 3-term
recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic
Yangians, Integrable Quantum Systems and Dorey's rule
We study tensor products of fundamental representations of Yangians and show
that the fundamental quotients of such tensor products are given by Dorey's
rule.Comment: We have made corrections to the results for the Yangians associated
to the non--simply laced algebra
New concept of relativistic invariance in NC space-time: twisted Poincar\'e symmetry and its implications
We present a systematic framework for noncommutative (NC) QFT within the new
concept of relativistic invariance based on the notion of twisted Poincar\'e
symmetry (with all 10 generators), as proposed in ref. [7]. This allows to
formulate and investigate all fundamental issues of relativistic QFT and offers
a firm frame for the classification of particles according to the
representation theory of the twisted Poincar\'e symmetry and as a result for
the NC versions of CPT and spin-statistics theorems, among others, discussed
earlier in the literature. As a further application of this new concept of
relativism we prove the NC analog of Haag's theorem.Comment: 15 page
CuO Elaboration and Studies of the Influence of Heat Treatment on the Structural Properties
In the present work we synthesize nano powders of CuO by precipitation method, using CuCl2 as precursor. The obtained powder has undergone a heat treatment annealing 100°C, and 450°C. Structural analysis by X-Ray diffraction, Fourier transform infrared (FTIR) microscopy and scanning electron microscopy (SEM) reveal that CuO nano particles are in nano graphs forms and with improved crystallization at 450°C, annealing temperature as monoclinic crystal lattice structure. The radius of NCs calculated by the Scherrer formula is 12.31 nm
Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
Let Uq(ghat) be the quantum affine algebra associated to a simply-laced
simple Lie algebra g. We examine the relationship between Dorey's rule, which
is a geometrical statement about Coxeter orbits of g-weights, and the structure
of q-characters of fundamental representations V_{i,a} of Uq(ghat). In
particular, we prove, without recourse to the ADE classification, that the rule
provides a necessary and sufficient condition for the monomial 1 to appear in
the q-character of a three-fold tensor product V_{i,a} x V_{j,b} x V_{k,c}.Comment: 30 pages, latex; v2, to appear in Communications in Mathematical
Physic
Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory
In this paper, using a Hopf-algebraic method, we construct deformed
Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this
twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can
see the consistency between the algebra and non(anti)commutative relation among
(super)coordinates and interpret that symmetry of non(anti)commutative QFT is
in fact twisted one. The key point is validity of our new twist element that
guarantees non(anti)commutativity of space. It is checked in this paper for N=1
case. We also comment on the possibility of noncommutative central charge
coordinate. Finally, because our twist operation does not break the original
algebra, we can claim that (twisted) SUSY is not broken in contrast to the
string inspired SUSY in N=1 non(anti)commutative superspace.Comment: 15 pages, LaTeX. v3:One section added, typos corrected, to appear in
Int. J. Mod. Phys.
A family of tridiagonal pairs and related symmetric functions
A family of tridiagonal pairs which appear in the context of quantum
integrable systems is studied in details. The corresponding eigenvalue
sequences, eigenspaces and the block tridiagonal structure of their matrix
realizations with respect the dual eigenbasis are described. The overlap
functions between the two dual basis are shown to satisfy a coupled system of
recurrence relations and a set of discrete second-order difference
equations which generalize the ones associated with the Askey-Wilson orthogonal
polynomials with a discrete argument. Normalizing the fundamental solution to
unity, the hierarchy of solutions are rational functions of one discrete
argument, explicitly derived in some simplest examples. The weight function
which ensures the orthogonality of the system of rational functions defined on
a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear
in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition
corrected compared to published versio
Universal Baxterization for -graded Hopf algebras
We present a method for Baxterizing solutions of the constant Yang-Baxter
equation associated with -graded Hopf algebras. To demonstrate the
approach, we provide examples for the Taft algebras and the quantum group
.Comment: 8 page
A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
In this paper, we construct a Q-operator as a trace of a representation of
the universal R-matrix of over an infinite-dimensional
auxiliary space. This auxiliary space is a four-parameter generalization of the
q-oscillator representations used previously. We derive generalized T-Q
relations in which 3 of these parameters shift. After a suitable restriction of
parameters, we give an explicit expression for the Q-operator of the 6-vertex
model and show the connection with Baxter's expression for the central block of
his corresponding operator.Comment: 22 pages, Latex2e. This replacement is a revised version that
includes a simple explicit expression for the Q matrix for the 6-vertex mode
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