A Positive integral property on the ground state of the two-boundary Temperley--Lieb Hamiltonian

Abstract

We study the two-boundary Temperley--Lieb $O(n)$ loop model on Kazhdan--Lusztig bases of type A and B. We obtain explicit expressions of the ground state of the two-boundary Temperley--Lieb Hamiltonian by means of a coideal subalgebra of $U_q({\mathfrak{sl}}_2)$. This ground state possesses a positive integral property. We conjecture that some components of the ground state are directly related to an enumeration of binary or permutation matrices.

62 pages

References in corpus (4)

• The two-boundary Temperley-Lieb algebra
• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• Kazhdan-Lusztig polynomials for the Hermitian symmetric pair $(B_N,A_{N-1})$
• Canonical bases of a coideal subalgebra in $U_q({\mathfrak{sl}}_2)$

Cited by in corpus (2)

• Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation
• Symmetric Dyck tilings, ballot tableaux and tree-like tableaux of shifted shapes