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22
Fermionic solution of the AndrewsBaxterForrester model I: Unification of TBA and . . .
, 1995
"... The problem of computing the onedimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grandcanonical 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 onedimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grandcanonical 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 AndrewsBailey Construction
, 1994
"... We prove qseries 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 qseries 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 AndrewsGordon identities and qmultinomial coefficients
 qalg/9601012, Comm. Math. Phys
"... We prove polynomial bosonfermion 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 qdeformations 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 bosonfermion 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 qdeformations of the coefficients of xa in the expansion of (1 + x + · · · + xk) L. A combinatorial interpretation for these qmultinomial coefficients is given using Durfee dissection partitions. The fermionic side of the polynomial identities arises as the partition function of a onedimensional latticegas 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, qMultinomials And Two Variants Of The AndrewsGordon Identities
"... A few years ago Foda, Quano, Kirillov and Warnaar proposed and proved various nite analogs of the celebrated AndrewsGordon 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 AndrewsGordon 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 AndrewsGordon identities. 1. Background and the first variant of the AndrewsGordon identities In 1961, Gordon [12] found a natural generalization of the RogersRamanujan 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 AndrewsGordon Identities
 E K H 1998 J. PHYS.: CONDENS. MATTER
"... The object of this paper is to propose and prove a new generalization of the AndrewsGordon 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 AndrewsGordon 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 FRACTIONALLEVEL STRING FUNCTIONS TO BAILEY’S LEMMA
, 1999
"... In this paper it is shown that the onedimensional 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 onedimensional 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 constantsign expressions for the onedimensional configuration sums, our result is employed to derive fermionic expressions for fractionallevel string functions, parafermion characters and A (1) 1 branching functions. In addition, qseries identities are obtained whose Lie algebraic and/or combinatorial interpretation is still lacking.
qtrinomial identities
 J. Math. Phys
, 1999
"... We obtain connection coefficients between qbinomial and qtrinomial coefficients. Using these, one can transform qbinomial identities into a qtrinomial 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 qbinomial and qtrinomial coefficients. Using these, one can transform qbinomial identities into a qtrinomial 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 qdimensions 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 RogersRamanujan type recursions
, 2004
"... In a previous paper [4] we generalized the RogersRamanujan identities by proving formulas for the Carlitz qFibonacci polynomials FnðtÞ which reduce to the finite version of the RogersRamanujan identities obtained by I. SCHUR for t 1. The qFibonacci 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 RogersRamanujan identities by proving formulas for the Carlitz qFibonacci polynomials FnðtÞ which reduce to the finite version of the RogersRamanujan identities obtained by I. SCHUR for t 1. The qFibonacci 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 RogersRamanujan type which are related to some identities by KIRILLOV [6] and FODA and QUANO [5].