Totally Symmetric Self-Complementary Plane Partitions and Quantum Knizhnik-Zamolodchikov equation: a conjecture

Abstract

We present a new conjecture relating the minimal polynomial solution of the level-one $U_q(\mathfrak{sl}(2))$ quantum Knizhnik-Zamolodchikov equation for generic values of $q$ in the link pattern basis and some $q$-enumeration of Totally Symmetric Self-Complementary Plane Partitions.

16 pages, 12 figures, uses lanlmac, epsf, mssymb

References in corpus (4)

• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Combinatorial nature of ground state vector of O(1) loop model
• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Gröbner geometry of Schubert polynomials

Cited by in corpus (13)

• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• Multiply-refined enumeration of alternating sign matrices
• Factorised solutions of Temperley-Lieb $q$KZ equations on a segment
• Finite-size corrections for universal boundary entropy in bond percolation
• A conjectured formula for Fully Packed Loop configurations in a triangle
• Grassmann-Grassmann conormal varieties, integrability, and plane partitions
• A bijectional attack on the Razumov-Stroganov conjecture
• Correlations in totally symmetric self-complementary plane partitions
• On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values
• A Catalan Subset of Descending Plane Partitions
• Higher Spin Alternating Sign Matrices