Box-Basket-Ball Systems
arXiv:1011.5930 · doi:10.1142/S0129055X12500195
Abstract
Using the whurl relation of the first two authors, we define a new discrete solitonic system, which we call the box-basket-ball system, generalizing the box-ball system of Takahashi and Satsuma. In box-basket-ball systems balls may be put either into boxes or into baskets. While boxes stay fixed, both balls and baskets get moved during time evolution. Balls and baskets behave as fermionic and bosonic particles respectively. We classify the solitons of this system, and study their scattering.
18 pages, 4 figures. (v2) introduction added; additional comments at section 5.4; final version. (v1) 16 pages, 4 figures
References in corpus (6)
- Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
- Tau functions in combinatorial Bethe ansatz
- Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
- Affine crystal structure on rigged configurations of type D_n^(1)
- Kirillov--Schilling--Shimozono bijection as energy functions of crystals
- Crystals and total positivity on orientable surfaces