Particle Content of the -configurations

  • Evgeny Mukhin

    Indiana University Purdue University Indianapolis, United States
  • Boris Feigin

    Independent University of Moscow, Russian Federation
  • M. Jimbo

    University of Tokyo, Japan
  • Tetsuji Miwa

    Kyoto University, Japan
  • Yoshihiro Takeyama

    Graduate School of Pure and Applied Sciences, Ibaraki, Japan


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

Evgeny Mukhin, Boris Feigin, M. Jimbo, Tetsuji Miwa, Yoshihiro Takeyama, Particle Content of the -configurations. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 163–220

DOI 10.2977/PRIMS/1145475969