Particle Content of the -configurations
Boris Feigin
Independent University of Moscow, Russian FederationMichio Jimbo
University of Tokyo, JapanTetsuji Miwa
Kyoto University, JapanEvgeny Mukhin
Indiana University Purdue University Indianapolis, United StatesYoshihiro Takeyama
Graduate School of Pure and Applied Sciences, Ibaraki, Japan
![Particle Content of the $(\boldsymbol k, 3)$-configurations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-prims-volume-40-issue-1.png&w=3840&q=90)
Abstract
For all , we construct a bijection between the set of sequences of non-negative integers satisfying and the set of rigged partitions . Here is a partition satisfying and is such that if . One can think of as the particle content of the configuration and as the energy level of the -th particle, which has the weight . The total energy is written as the sum of the two-body interaction term and the free part . The bijection implies a fermionic formula for the one-dimensional configuration sums . We also derive the polynomial identities which describe the configuration sums corresponding to the configurations with prescribed values for and , and such that for all .
Cite this article
Boris Feigin, Michio Jimbo, Tetsuji Miwa, Evgeny Mukhin, Yoshihiro Takeyama, Particle Content of the -configurations. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 163–220
DOI 10.2977/PRIMS/1145475969