Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
43 (2002), S. 4135-4146
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at Δ=−1/2 and various symmetry classes of alternating sign matrices. Here we use the integrability of the XXZ chain to gain further insight into these developments. In doing so we obtain a number of new results using Baxter's Q function for the XXZ chain for periodic, twisted and open boundary conditions. These include expressions for the elementary symmetric functions evaluated at the ground state solution of the Bethe roots. In this approach Schur functions play a central role and enable us to derive determinant expressions which appear in certain natural double products over the Bethe roots. When evaluated these give rise to the numbers counting different symmetry classes of alternating sign matrices. © 2002 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1487445
Permalink
|
Location |
Call Number |
Expected |
Availability |