Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583980 | Journal of Algebra | 2016 | 56 Pages |
Abstract
We give a bijection Φ from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals of the form Br,1Br,1 and B1,sB1,s in type D4(3). We show that the cocharge statistic is sent to the energy statistic for tensor products ⨂i=1NBri,1 and ⨂i=1NB1,si. We extend this bijection to a single Br,sBr,s, show that it preserves statistics, and obtain the so-called Kirillov–Reshetikhin tableaux model for Br,sBr,s. Additionally, we show that Φ commutes with the virtualization map and that B1,sB1,s is naturally a virtual crystal in type D4(1), thus defining an affine crystal structure on rigged configurations corresponding to B1,sB1,s.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Travis Scrimshaw,