On some ground state components of the O(1) loop model

Abstract

We address a number of conjectures about the ground state O(1) loop model, computing in particular two infinite series of partial sums of its entries and relating them to the enumeration of plane partitions. Our main tool is the use of integral formulae for a polynomial solution of the quantum Knizhnik-Zamolodchikov equation.

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References in corpus (5)

• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• Quantum incompressibility and Razumov Stroganov type conjectures

Cited by in corpus (2)

• Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identities
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations