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22
Fermionic solution of the Andrews-Baxter-Forrester model I: Unification of TBA and . . .
, 1995
"... The problem of computing the one-dimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grand-canonical partition function of a gas of charged particles obeying certain fermionic exclusion rules. We thus obtain a new fermionic method to compute the ..."
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Cited by 44 (15 self)
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The problem of computing the one-dimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grand-canonical partition function of a gas of charged particles obeying certain fermionic exclusion rules. We thus obtain a new fermionic method to compute the local height probabilities of the model. Combined with the original bosonic approach of Andrews, Baxter and Forrester, we obtain a new proof of (some of) Melzer’s polynomial identities. In the infinite limit these identities yield Rogers– Ramanujan type identities for the Virasoro characters χ (r−1,r) 1,1 (q) as conjectured by the Stony Brook group. As a result of our working the corner transfer matrix and thermodynamic Bethe Ansatz approaches to solvable lattice models are unified.
Virasoro character Identities from the Andrews-Bailey Construction
, 1994
"... We prove q-series identities between bosonic and fermionic representations of certain Virasoro characters. These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews’ extensions of Bailey’s lemma to recently obtained ..."
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Cited by 28 (3 self)
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We prove q-series identities between bosonic and fermionic representations of certain Virasoro characters. These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews’ extensions of Bailey’s lemma to recently obtained polynomial identities.
The Andrews-Gordon identities and q-multinomial coefficients
- q-alg/9601012, Comm. Math. Phys
"... We prove polynomial boson-fermion identities for the generating function of the number of partitions of n of the form n = ∑L−1 j=1 jfj, with f1 ≤ i−1, fL−1 ≤ i ′ −1 and fj +fj+1 ≤ k. The bosonic side of the identities involves q-deformations of the coefficients of xa in the expansion of (1 + x + · ..."
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Cited by 28 (8 self)
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We prove polynomial boson-fermion identities for the generating function of the number of partitions of n of the form n = ∑L−1 j=1 jfj, with f1 ≤ i−1, fL−1 ≤ i ′ −1 and fj +fj+1 ≤ k. The bosonic side of the identities involves q-deformations of the coefficients of xa in the expansion of (1 + x + · · · + xk) L. A combinatorial interpretation for these q-multinomial coefficients is given using Durfee dissection partitions. The fermionic side of the polynomial identities arises as the partition function of a one-dimensional lattice-gas of fermionic particles. In the limit L → ∞, our identities reproduce the analytic form of Gordon’s generalization of the Rogers–Ramanujan identities, as found by Andrews. Using the q → 1/q duality, identities are obtained for branching functions corresponding to cosets of type (A (1) 1)k ×(A (1) (1) 1)ℓ/(A 1)k+ℓ of fractional level ℓ.
Lattice Paths, q-Multinomials And Two Variants Of The Andrews-Gordon Identities
"... A few years ago Foda, Quano, Kirillov and Warnaar proposed and proved various nite analogs of the celebrated Andrews-Gordon identities. In this paper we use these polynomial identities along with the combinatorial techniques introduced in our recent paper to derive Garrett, Ismail, Stanton type form ..."
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Cited by 16 (1 self)
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A few years ago Foda, Quano, Kirillov and Warnaar proposed and proved various nite analogs of the celebrated Andrews-Gordon identities. In this paper we use these polynomial identities along with the combinatorial techniques introduced in our recent paper to derive Garrett, Ismail, Stanton type formulas for two variants of the Andrews-Gordon identities. 1. Background and the first variant of the Andrews-Gordon identities In 1961, Gordon [12] found a natural generalization of the Rogers-Ramanujan partition theorem. Theorem 1. (Gordon) For all 1, 0 s , the partitions of N of the frequency form N = P j1 jf j with f 1 s and f j +f j+1 , f j 0 (for all j 1) are equinumerous with the partitions of N into parts not congruent to 0 or (s+1) modulo 2 + 3. Thirteen years later, Andrews [1] proposed and proved the following analytic counterpart to Gordon's theorem: Theorem 2. (Andrews) For all ; s as in Theorem 1, and jqj < 1, X n1 ;n2 ;:::;n 0 q N 2 1 +:::...
Variants Of The Andrews-Gordon Identities
- E K H 1998 J. PHYS.: CONDENS. MATTER
"... The object of this paper is to propose and prove a new generalization of the Andrews-Gordon Identities, extending a recent result of Garrett, Ismail and Stanton. We also give a combinatorial discussion of the nite form of their result which appeared in the work of Andrews, Knopfmacher, and Paule. ..."
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Cited by 9 (2 self)
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The object of this paper is to propose and prove a new generalization of the Andrews-Gordon Identities, extending a recent result of Garrett, Ismail and Stanton. We also give a combinatorial discussion of the nite form of their result which appeared in the work of Andrews, Knopfmacher, and Paule.
Conjugate Bailey Pairs. FROM CONFIGURATION SUMS AND FRACTIONAL-LEVEL STRING FUNCTIONS TO BAILEY’S LEMMA
, 1999
"... In this paper it is shown that the one-dimensional configuration sums of the solvable lattice models of Andrews, Baxter and Forrester and the string functions associated with admissible representations of the affine Lie algebra A (1) 1 as introduced by Kac and Wakimoto can be exploited to yield a ve ..."
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Cited by 8 (4 self)
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In this paper it is shown that the one-dimensional configuration sums of the solvable lattice models of Andrews, Baxter and Forrester and the string functions associated with admissible representations of the affine Lie algebra A (1) 1 as introduced by Kac and Wakimoto can be exploited to yield a very general class of conjugate Bailey pairs. Using the recently established fermionic or constant-sign expressions for the one-dimensional configuration sums, our result is employed to derive fermionic expressions for fractionallevel string functions, parafermion characters and A (1) 1 branching functions. In addition, q-series identities are obtained whose Lie algebraic and/or combinatorial interpretation is still lacking.
q-trinomial identities
- J. Math. Phys
, 1999
"... We obtain connection coefficients between q-binomial and q-trinomial coefficients. Using these, one can transform q-binomial identities into a q-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theor ..."
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Cited by 6 (3 self)
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We obtain connection coefficients between q-binomial and q-trinomial coefficients. Using these, one can transform q-binomial identities into a q-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the φ2,1 and φ1,5 perturbations of minimal conformal field theory. 1
SPINON BASIS FOR ( ̂ sl2)k INTEGRABLE HIGHEST WEIGHT MODULES AND NEW CHARACTER FORMULAS
, 1995
"... In this note we review the spinon basis for the integrable highest weight modules of ̂sl2 at levels k≥1, and give the corresponding character formula. We show that our spinon basis is intimately related to the basis proposed by Foda et al. in the principal gradation of the algebra. This gives rise t ..."
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Cited by 5 (0 self)
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In this note we review the spinon basis for the integrable highest weight modules of ̂sl2 at levels k≥1, and give the corresponding character formula. We show that our spinon basis is intimately related to the basis proposed by Foda et al. in the principal gradation of the algebra. This gives rise to new identities for the q-dimensions of the integrable modules. (to appear in the Proceedings of ‘Statistical Mechanics and Quantum Field Theory, ’ USC, May 16–21, 1994) 1.
A class of Rogers-Ramanujan type recursions
, 2004
"... In a previous paper [4] we generalized the Rogers-Ramanujan identities by proving formulas for the Carlitz q-Fibonacci polynomials FnðtÞ which reduce to the finite version of the Rogers-Ramanujan identities obtained by I. SCHUR for t 1. The q-Fibonacci polynomials can be interpreted as the weight ..."
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Cited by 5 (5 self)
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In a previous paper [4] we generalized the Rogers-Ramanujan identities by proving formulas for the Carlitz q-Fibonacci polynomials FnðtÞ which reduce to the finite version of the Rogers-Ramanujan identities obtained by I. SCHUR for t 1. The q-Fibonacci polynomials can be interpreted as the weight of a set of lattice paths in R2 which are contained in the strip 2 y 1. In this paper we extend these results to lattice paths contained in more general strips. We determine the recursions satisfied by the corresponding polynomials and derive identities of the Rogers-Ramanujan type which are related to some identities by KIRILLOV [6] and FODA and QUANO [5].
