Kirillov--Schilling--Shimozono bijection as energy functions of crystals

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dc.creatorSakamoto, Reiho
dc.date2007-11-27
dc.date2008-10-30
dc.date.accessioned2026-07-07T12:44:29Z
dc.date.available2026-07-07T12:44:29Z
dc.descriptionThe Kirillov--Schilling--Shimozono (KSS) bijection appearing in theory of the Fermionic formula gives an one to one correspondence between the set of elements of tensor products of the Kirillov--Reshetikhin crystals (called paths) and the set of rigged configurations. It is a generalization of Kerov--Kirillov--Reshetikhin bijection and plays inverse scattering formalism for the box-ball systems. In this paper, we give an algebraic reformulation of the KSS map from the paths to rigged configurations, using the combinatorial R and energy functions of crystals. It gives a characterization of the KSS bijection as an intrinsic property of tensor products of crystals.
dc.description31 pages, final version, expositions much detailed
dc.identifierhttps://arxiv.org/abs/0711.4185
dc.identifierhttp://arxiv.org/abs/0711.4185
dc.identifierInternational Mathematics Research Notices (2009) 2009: 579-614
dc.identifierdoi:10.1093/imrn/rnn140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220786
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.titleKirillov--Schilling--Shimozono bijection as energy functions of crystals
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