2,432 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
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
Dynamic Body VSLAM with Semantic Constraints
Image based reconstruction of urban environments is a challenging problem
that deals with optimization of large number of variables, and has several
sources of errors like the presence of dynamic objects. Since most large scale
approaches make the assumption of observing static scenes, dynamic objects are
relegated to the noise modeling section of such systems. This is an approach of
convenience since the RANSAC based framework used to compute most multiview
geometric quantities for static scenes naturally confine dynamic objects to the
class of outlier measurements. However, reconstructing dynamic objects along
with the static environment helps us get a complete picture of an urban
environment. Such understanding can then be used for important robotic tasks
like path planning for autonomous navigation, obstacle tracking and avoidance,
and other areas. In this paper, we propose a system for robust SLAM that works
in both static and dynamic environments. To overcome the challenge of dynamic
objects in the scene, we propose a new model to incorporate semantic
constraints into the reconstruction algorithm. While some of these constraints
are based on multi-layered dense CRFs trained over appearance as well as motion
cues, other proposed constraints can be expressed as additional terms in the
bundle adjustment optimization process that does iterative refinement of 3D
structure and camera / object motion trajectories. We show results on the
challenging KITTI urban dataset for accuracy of motion segmentation and
reconstruction of the trajectory and shape of moving objects relative to ground
truth. We are able to show average relative error reduction by a significant
amount for moving object trajectory reconstruction relative to state-of-the-art
methods like VISO 2, as well as standard bundle adjustment algorithms
On minimal affinizations of representations of quantum groups
In this paper we study minimal affinizations of representations of quantum
groups (generalizations of Kirillov-Reshetikhin modules of quantum affine
algebras introduced by Chari). We prove that all minimal affinizations in types
A, B, G are special in the sense of monomials. Although this property is not
satisfied in general, we also prove an analog property for a large class of
minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin
algorithm works for these modules. For minimal affinizations of type A, B we
prove the thin property (the l-weight spaces are of dimension 1) and a
conjecture of Nakai-Nakanishi (already known for type A). The proof of the
special property is extended uniformly for more general quantum affinizations
of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for
publication in Communications in Mathematical Physic
Low Power High Gain Op-Amp using Square Root based Current Generator
A very high gain two stage CMOS operational amplifier has been presented The proposed circuit is implemented in 180nm CMOS technology with a supply voltage of 0 65V The current source in the OPAMP is replaced by a square root based current generator which helps to reduce the impact of process variations on the circuit and low power consumption due to the operation of MOS in subthreshold region So with the help of square root based current generator the better controllability over gain can be obtained The proposed opamp shows a high gain of 121 9dB and low power consumption of 11 89uW is achieve
6J Symbols Duality Relations
It is known that the Fourier transformation of the square of (6j) symbols has
a simple expression in the case of su(2) and U_q(su(2)) when q is a root of
unit. The aim of the present work is to unravel the algebraic structure behind
these identities. We show that the double crossproduct construction H_1\bowtie
H_2 of two Hopf algebras and the bicrossproduct construction H_2^{*}\lrbicross
H_1 are the Hopf algebras structures behind these identities by analysing
different examples. We study the case where D= H_1\bowtie H_2 is equal to the
group algebra of ISU(2), SL(2,C) and where D is a quantum double of a finite
group, of SU(2) and of U_q(su(2)) when q is real.Comment: 28 pages, 2 figure
Langlands duality for finite-dimensional representations of quantum affine algebras
We describe a correspondence (or duality) between the q-characters of
finite-dimensional representations of a quantum affine algebra and its
Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this
duality for the Kirillov-Reshetikhin modules and their irreducible tensor
products. In the course of the proof we introduce and construct "interpolating
(q,t)-characters" depending on two parameters which interpolate between the
q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for
publication in Letters in Mathematical Physic
The quantum bialgebra associated with the eight-vertex R-matrix
The quantum bialgebra related to the Baxter's eight-vertex R-matrix is found
as a quantum deformation of the Lie algebra of sl(2)-valued automorphic
functions on a complex torus.Comment: 4 page
Progress in Solving the 3-Dimensional Inversion Problem for Eddy Current NDE
The eddy current NDE inversion problem is to determine the parameters of a flaw from the measured eddy current sensor impedance changes. Mathematically, this requires finding the transformation which gives the sensor impedance changes in terms of the flaw parameters, and then inverting this transformation. Finding the transformation is called the forward problem, and finding the inverse of the transformation is equivalent to the inversion problem. The principal difficulty in solving the forward problem is finding solutions to Maxwell\u27s equations in the complex geometries involved. This paper describes a solution to the forward problem which is valid for ellipsoidal shaped void flaws in a non-magnetic conductor, and for flaw dimensions such that the incident field variations are at most linear over the region occupied by the flaw
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