2 research outputs found
Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
We present a necessary and sufficient condition for a finite-dimensional
highest weight representation of the loop algebra to be irreducible. In
particular, for a highest weight representation with degenerate parameters of
the highest weight, we can explicitly determine whether it is irreducible or
not. We also present an algorithm for constructing finite-dimensional highest
weight representations with a given highest weight. We give a conjecture that
all the highest weight representations with the same highest weight can be
constructed by the algorithm. For some examples we show the conjecture
explicitly. The result should be useful in analyzing the spectra of integrable
lattice models related to roots of unity representations of quantum groups, in
particular, the spectral degeneracy of the XXZ spin chain at roots of unity
associated with the loop algebra.Comment: 32 pages with no figure; with corrections on the published versio
Lattice fermion models with supersymmetry
We investigate a family of lattice models with manifest N=2 supersymmetry.
The models describe fermions on a 1D lattice, subject to the constraint that no
more than k consecutive lattice sites may be occupied. We discuss the special
properties arising from the supersymmetry, and present Bethe ansatz solutions
of the simplest models. We display the connections of the k=1 model with the
spin-1/2 antiferromagnetic XXZ chain at \Delta=-1/2, and the k=2 model with
both the su(2|1)-symmetric tJ model in the ferromagnetic regime and the
integrable spin-1 XXZ chain at \Delta=-1/\sqrt{2}. We argue that these models
include critical points described by the superconformal minimal models.Comment: 28 pages. v2: added new result on mapping to XXZ chai