Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On quantum group symmetry and Bethe ansatz for the asymmetric twin spin
  chain with integrable boundary   Motivated by a study of the crossing symmetry of the `gemini' representation
of the affine Hecke algebra we give a construction for crossing tensor space
representations of ordinary Hecke algebras. These representations build
solutions to the Yang--Baxter equation satisfying the crossing condition (that
is, integrable quantum spin chains). We show that every crossing representation
of the Temperley--Lieb algebra appears in this construction, and in particular
that this construction builds new representations. We extend these to new
representations of the blob algebra, which build new solutions to the Boundary
Yang--Baxter equation (i.e. open spin chains with integrable boundary
conditions).
  We prove that the open spin chain Hamiltonian derived from Sklyanin's
commuting transfer matrix using such a solution can always be expressed as the
representation of an element of the blob algebra, and determine this element.
We determine the representation theory (irreducible content) of the new
representations and hence show that all such Hamiltonians have the same
spectrum up to multiplicity, for any given value of the algebraic boundary
parameter. (A corollary is that our models have the same spectrum as the open
XXZ chain with nondiagonal boundary -- despite differing from this model in
having reference states.) Using this multiplicity data, and other ideas, we
investigate the underlying quantum group symmetry of the new Hamiltonians. We
derive the form of the spectrum and the Bethe ansatz equations.

6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg