Paths, Crystals and Fermionic Formulae

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dc.creatorHatayama, G.
dc.creatorKuniba, A.
dc.creatorOkado, M.
dc.creatorTakagi, T.
dc.creatorTsuboi, Z.
dc.date2001-02-15
dc.date.accessioned2026-07-07T04:40:10Z
dc.date.available2026-07-07T04:40:10Z
dc.descriptionWe introduce a fermionic formula associated with any quantum affine algebra U_q(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^{(1)}_2-module related to the embedding G^{(1)}_2 \hookrightarrow B^{(1)}_3 \hookrightarrow D^{(1)}_4.
dc.descriptionLaTeX2e, 68 pages, no figure
dc.identifierhttps://arxiv.org/abs/math/0102113
dc.identifierhttp://arxiv.org/abs/math/0102113
dc.identifierProg.Math.Phys. 23 (2002) 205-272
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60944
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.subjectPrimary 81R10, 81R50, 82B23; Secondary 05E15
dc.titlePaths, Crystals and Fermionic Formulae
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