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Mathematics > Quantum Algebra

arXiv:0711.4185 (math)
[Submitted on 27 Nov 2007 (v1), last revised 30 Oct 2008 (this version, v2)]

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

Authors:Reiho Sakamoto
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Abstract: The 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.
Comments: 31 pages, final version, expositions much detailed
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)
Cite as: arXiv:0711.4185 [math.QA]
  (or arXiv:0711.4185v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.0711.4185
Journal reference: International Mathematics Research Notices (2009) 2009: 579-614
Related DOI: https://doi.org/10.1093/imrn/rnn140

Submission history

From: Reiho Sakamoto [view email]
[v1] Tue, 27 Nov 2007 06:06:11 UTC (23 KB)
[v2] Thu, 30 Oct 2008 05:16:23 UTC (27 KB)
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