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Remarks on Fermionic Formula
Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the…
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Paths, crystals and fermionic formulae
We introduce a fermionic formula associated with any quantum affine algebra U q (X N (r) . Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable lattice models, we…
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T-systems and Y-systems in integrable systems
T- and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable…
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FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS II: APPLICATIONS
Reported are two applications of the functional relations (T system) among a commuting family of row-to-row transfer matrices proposed in the previous paper (Part I). For a general simple Lie algebra…
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Exactly Solvable SOS Models II: Proof of the star-triangle relation and combinatorial identities
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Exactly solvable SOS models: local height probabilities and theta function identities
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The AM(1) automata related to crystals of symmetric tensors
A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra Uq′(AM(1)) is introduced. It is a crystal theoretic formulation of the…
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Tetrahedron equation and generalized quantum groups
We construct 2 n ?> -families of solutions of the Yang–Baxter equation from n-products of three-dimensional R and L operators satisfying the tetrahedron equation. They are identified with the quantum…
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Analytic Bethe ansatz for fundamental representations of Yangians
We study the analytic Bethe, ansatz in solvable vertex models associated with the YangianY(Xr) or its quantum affine analogueUq(Xr(1)) forXr=Br,Cr andDr. Eigenvalue formulas are proposed for the…
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A Common Structure in PBW Bases of the Nilpotent Subalgebra of U_q(g) and Quantized Algebra of Functions
For a finite-dimensional simple Lie algebra g, let U + q (g) be the positive part of the quantized universal enveloping algebra, and Aq(g) be the quantized algebra of functions. We show that the…
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