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1.
Atsuo Kuniba Tomoki Nakanishi Zengo Tsuboi 《Communications in Mathematical Physics》2002,227(1):155-190
We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum
mechanical models. We call them the finite and infinite $Q$-systems according to the number of functions and equations. The
finite Q-systems appear as the thermal equilibrium conditions (the Sutherland–Wu equation) for certain statistical mechanical systems.
Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras.
We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp.
infinite) Q-system. As an application, we reformulate the Kirillov–Reshetikhin conjecture on the multiplicities formula of the KR modules
in terms of the canonical solutions of Q-systems.
Received: 2 August 2001 / Accepted: 27 December 2001 相似文献
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We study the analytic Bethe, ansatz in solvable vertex models associated with the YangianY(X
r
) or its quantum affine analogueU
q
(X
r
(1)
) forX
r
=B
r
,C
r
andD
r
. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations ofY(X
r
). Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying theT-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms of Yangian analogues of the semi-standard Young tableaux. 相似文献
4.
Presented here is the construction of solvable two-dimensional lattice models associated with the affine Lie algebraA
n
/(1)
and an arbitrary pair of Young diagrams. The models comprise two kinds of fluctuation variables; one lives on the sites and takes on dominant integral weights of a fixed level, the other lives on edges and assumes the weights of the representations ofsl(n+1, C) specified by Young diagrams. The Boltzmann weights are elliptic solutions of the Yang-Baxter equation. Some conjectures on the one point functions are put forth. 相似文献
5.
A. Kuniba 《Theoretical and Mathematical Physics》2016,189(1):1472-1485
We survey the matrix product solutions of the Yang–Baxter equation recently obtained from the tetrahedron equation. They form a family of quantum R-matrices of generalized quantum groups interpolating the symmetric tensor representations of Uq(An?1(1)) and the antisymmetric tensor representations of \({U_{ - {q^{ - 1}}}}\left( {A_{n - 1}^{\left( 1 \right)}} \right)\). We show that at q = 0, they all reduce to the Yang–Baxter maps called combinatorial R-matrices and describe the latter by an explicit algorithm. 相似文献
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9.
The spectral decomposition of the path space of the vertex model associated
to the vector representation of the quantized affine algebra
is studied. We give a one-to-one correspondence between
the spin configurations and the semistandard tableaux of skew Young diagrams.
As a result we obtain a formula of the characters for the degeneracy of the
spectrum in terms of skew Schur functions. We conjecture that our
result describes the -module contents
of the Yangian -module structures of the level 1 integrable modules of the affine Lie algebra .
An analogous result is obtained also for a vertex model
associated to the quantized twisted affine
algebra , where characters
appear for the degeneracy of the spectrum.
The relations to the spectrum of the Haldane-Shastry and
the Polychronakos
models are also discussed.
Received: 28 July 1996 / Accepted: 11 October 1996 相似文献
10.
We construct a q-boson representation of the Zamolodchikov-Faddeev algebra whose structure function is given by the stochastic R matrix of \(U_q(A^{(1)}_n)\) introduced recently. The representation involves quantum dilogarithm type infinite products in the \(n(n-1)/2\)-fold tensor product of q-bosons. It leads to a matrix product formula of the stationary probabilities in the \(U_q(A_n^{(1)})\)-zero range process on a one-dimensional periodic lattice. 相似文献