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SIGMA 3 (2007), 009, 19 pages math-ph/0606040
https://doi.org/10.3842/SIGMA.2007.009
Contribution to the Vadim Kuznetsov Memorial Issue
Asymmetric Twin Representation: the Transfer Matrix Symmetry
Anastasia Doikou
INFN Section of Bologna, Physics Department, University of Bologna,
Via Irnerio 46, 40126 Bologna, Italy
Received August 02, 2006, in final form December 26, 2006; Published online January 09, 2007
Abstract
The symmetry of the Hamiltonian describing the asymmetric
twin model was partially studied in earlier works, and our aim here
is to generalize these results for the open transfer matrix. In this
spirit we first prove, that the so called boundary quantum algebra
provides a symmetry for any generic - independent of the choice of
model - open transfer matrix with a trivial left boundary. In
addition it is shown that the boundary quantum algebra is the
centralizer of the B type Hecke algebra. We then focus on the
asymmetric twin representation of the boundary Temperley-Lieb
algebra. More precisely, by exploiting exchange relations dictated
by the reflection equation we show that the transfer matrix with
trivial boundary conditions enjoys the recognized
Uq(sl2) Ä
Ui(sl2) symmetry. When
a non-diagonal boundary is implemented the symmetry as expected is
reduced, however again certain familiar boundary non-local charges
turn out to commute with the corresponding transfer matrix.
Key words:
quantum integrability; boundary symmetries; quantum algebras; Hecke algebras.
pdf (343 kb)
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