A bijection between type D_n^{(1)} crystals and rigged configurations

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dc.creatorSchilling, Anne
dc.date2004-06-12
dc.date2004-12-19
dc.date.accessioned2026-07-07T06:22:43Z
dc.date.available2026-07-07T06:22:43Z
dc.descriptionHatayama et al. conjectured fermionic formulas associated with tensor products of U'_q(g)-crystals B^{r,s}. The crystals B^{r,s} correspond to the Kirillov--Reshetikhin modules which are certain finite dimensional U'_q(g)-modules. In this paper we present a combinatorial description of the affine crystals B^{r,1} of type D_n^{(1)}. A statistic preserving bijection between crystal paths for these crystals and rigged configurations is given, thereby proving the fermionic formula in this case. This bijection reflects two different methods to solve lattice models in statistical mechanics: the corner-transfer-matrix method and the Bethe Ansatz.
dc.description38 pages; version to appear in J. Algebra
dc.identifierhttps://arxiv.org/abs/math/0406248
dc.identifierhttp://arxiv.org/abs/math/0406248
dc.identifierJ.Algebra 285 (2005) 292-334
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95992
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subject05A19; 05E99; 17B37; 81R50; 82B23
dc.titleA bijection between type D_n^{(1)} crystals and rigged configurations
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