Bailey flows and Bose-Fermi identities for the conformal coset models (A1(1))N × (A1(1))N′/(A1(1))N+N′

Berkovich, Alexander; McCoy, Barry M.; Schilling, Anne; Warnaar, S. Ole

doi:10.1016/s0550-3213(97)82955-0

Cited by 23 publications

(29 citation statements)

References 52 publications

(83 reference statements)

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“…Solvable RSOS models at a generic primitive root of unity give rise to yet further 1dsums associated with complicated energy functions. A typical example is [FB] corresponding to A (1) 1 , and as noted in Section 1.1, intricate arithmetic structures have been worked out on the fermionic formula and relation to fractional level representations [BMS,BMSW,FW2]. The crystal theory has not yet been adapted to such situations.…”

Section: Contents Of the Papermentioning

confidence: 99%

Paths, Crystals and Fermionic Formulae

Hatayama

Kuniba

Okado

et al. 2002

MathPhys Odyssey 2001

129

286

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We introduce a fermionic formula associated with any quantum affine algebra Uq(X (r) N ). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to representation theory, most crucially, the crystal basis theory. They include one dimensional sums over both finite and semi-infinite paths, spinon character formulae, Lepowski-Primc type conjectural formula for vacuum string functions, dilogarithm identities, Q-systems and their solution by characters of various classical subalgebras and so forth. The results expand [HKOTY1] including the twisted cases and more details on inhomogeneous paths consisting of non-perfect crystals. As a most intriguing example, certain inhomogeneous one dimensional sums conjecturally give rise to branching functions of an integrable G

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Section: Contents Of the Papermentioning

confidence: 99%

Paths, Crystals and Fermionic Formulae

Hatayama

Kuniba

Okado

et al. 2002

MathPhys Odyssey 2001

129

286

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“…This kind of phenomena have been conjectured or proved for a variety of setting and a wide class of representations. There are immense literatures on this, see for example [Ber,BMS,BMSW,BLS,DF,DKKMM,FLW,FOW,FS,Ge,HKKOTY,KM,Ki3,KR1,KSS,NRT,OPW,SW,Wa] and the reference therein. Especially there are extensive results on fractional level case of A (1) 1 cf.…”

Section: Introductionmentioning

confidence: 99%

Remarks on fermionic formula

Hatayama¹,

Yamada²,

Okado³

et al. 1999

Contemporary Mathematics

152

329

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Abstract. 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 fermionic formulae associated with general non-twisted quantum affine algebra Uq(X (1) n ) and discuss several aspects related to representation theories and combinatorics. They include crystal base theory, one dimensional sums, spinon character formulae, Q-system and combinatorial completeness of the string hypothesis for arbitrary Xn.

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“…(L, b; q) for p < p ′ < 2p and r = b = 1 are not given in [6,7]. A formula however does appear in [26].…”

Section: Resultsmentioning

confidence: 99%

“…It suffices for the purpose of this paper to state the fermionic formula for the case p < p ′ < 2p with p and p ′ relatively prime and r, s being pure Takahashi length. We follow [7,Section 4]. The fermionic formula depends on the continued fraction decomposition p…”

Section: Fermionic Formulas Formentioning

confidence: 99%