An Izergin–korepin-type Identity for the 8vsos Model, with Applications to Alternating Sign Matrices
نویسنده
چکیده
We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin– Korepin formula for the six-vertex model. As applications, we find dynamical (in the sense of the dynamical Yang–Baxter equation) generalizations of the enumeration and 2-enumeration of alternating sign matrices. The dynamical enumeration has a nice interpretation in terms of three-colourings of the square lattice.
منابع مشابه
On the weighted enumeration of alternating sign matrices and descending plane partitions
We prove a conjecture of Mills, Robbins and Rumsey [Alternating sign matrices and descending plane partitions, J. Combin. Theory Ser. A 34 (1983), 340–359] that, for any n, k, m and p, the number of n × n alternating sign matrices (ASMs) for which the 1 of the first row is in column k + 1 and there are exactly m −1’s and m+ p inversions is equal to the number of descending plane partitions (DPP...
متن کاملNonstandard coproducts and the Izergin-Korepin open spin chain
Corresponding to the Izergin-Korepin (A (2) 2 ) R matrix, there are three diagonal solutions (“K matrices”) of the boundary Yang-Baxter equation. Using these R and K matrices, one can construct transfer matrices for open integrable quantum spin chains. The transfer matrix corresponding to the identity matrix K = I is known to have Uq(o(3)) symmetry. We argue here that the transfer matrices corr...
متن کاملRazumov–Stroganov sum rule: a proof based on multi-parameter generalizations
We prove that the sum of entries of the suitably normalized groundstate vector of the O(1) loop model with periodic boundary conditions on a periodic strip of size 2n is equal to the total number of n× n alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the O(1) model with the partition function of the inhomogeneous six-vertex mod...
متن کاملProof of the Refined Alternating Sign Matrix Conjecture
Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order n equals A(n) := 1!4!7! · · · (3n − 2)! n!(n + 1)! · · · (2n − 1)! . Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) ‘1’ of the first row is at the rth column equals A(n) `n+r−2 n−1 ́`2n−1−r n−1 ́ `3n−2 n−1 ́ . Standing on...
متن کاملLink invariant of the Izergin–Korepin model
The link invariant associated with the Izergin–Korepin 19-vertex model is deduced using the method of statistical mechanics. It is shown that the Izergin–Korepin model leads to an invariant which is precisely the 3-state Akutsu–Wadati polynomial, previously known only for 2and 3-braid knots. We give a table of the invariant for all knots and links up to seven crossings.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008