2,393 research outputs found
Many-spinon states and the secret significance of Young tableaux
We establish a one-to-one correspondence between the Young tableaux
classifying the total spin representations of N spins and the exact eigenstates
of the the Haldane-Shastry model for a chain with N sites classified by the
total spins and the fractionally spaced single-particle momenta of the spinons.Comment: 4 pages, 3 figure
Representations of Double Affine Lie algebras
We study representations of the double affine Lie algebra associated to a
simple Lie algebra. We construct a family of indecomposable integrable
representations and identify their irreducible quotients. We also give a
condition for the indecomposable modules to be irreducible, this is analogous
to a result in the representation theory of quantum affine algebras. Finally,
in the last section of the paper, we show, by using the notion of fusion
product, that our modules are generically reducible
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
The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
An S-matrix satisying the Yang-Baxter equation with symmetries relevant to
the AdS_5xS^5 superstring has recently been determined up to an unknown scalar
factor. Such scalar factors are typically fixed using crossing relations,
however due to the lack of conventional relativistic invariance, in this case
its determination remained an open problem.
In this paper we propose an algebraic way to implement crossing relations for
the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a
Hopf-algebraic formulation of crossing in terms of the antipode and introduce
generalized rapidities living on the universal cover of the parameter space
which is constructed through an auxillary, coupling constant dependent,
elliptic curve. We determine the crossing transformation and write functional
equations for the scalar factor of the S-matrix in the generalized rapidity
plane.Comment: 27 pages, no figures; v2: sign typo fixed in (24), everything else
unchange
Pure O-sequences and matroid h-vectors
We study Stanley's long-standing conjecture that the h-vectors of matroid
simplicial complexes are pure O-sequences. Our method consists of a new and
more abstract approach, which shifts the focus from working on constructing
suitable artinian level monomial ideals, as often done in the past, to the
study of properties of pure O-sequences. We propose a conjecture on pure
O-sequences and settle it in small socle degrees. This allows us to prove
Stanley's conjecture for all matroids of rank 3. At the end of the paper, using
our method, we discuss a first possible approach to Stanley's conjecture in
full generality. Our technical work on pure O-sequences also uses very recent
results of the third author and collaborators.Comment: Contains several changes/updates with respect to the previous
version. In particular, a discussion of a possible approach to the general
case is included at the end. 13 pages. To appear in the Annals of
Combinatoric
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
The Application of Finite Element Method Analysis to Eddy Current NDE
The Finite Element Method for the computation of eddy current fields is presented. The method is described for geometries with a one component eddy current field. The use of the method for the calculation of the impedance of eddy current sensors in the vicinity of defects is shown. An example is given of the method applied to a C-magnet type sensor positioned over a crack in a plane conducting material
Factorizing twists and R-matrices for representations of the quantum affine algebra U_q(\hat sl_2)
We calculate factorizing twists in evaluation representations of the quantum
affine algebra U_q(\hat sl_2). From the factorizing twists we derive a
representation independent expression of the R-matrices of U_q(\hat sl_2).
Comparing with the corresponding quantities for the Yangian Y(sl_2), it is
shown that the U_q(\hat sl_2) results can be obtained by `replacing numbers by
q-numbers'. Conversely, the limit q -> 1 exists in representations of U_q(\hat
sl_2) and both the factorizing twists and the R-matrices of the Yangian Y(sl_2)
are recovered in this limit.Comment: 19 pages, LaTe
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