Difference Hierarchies for n T I" -functions

Darlayne Addabbo, Maarten Bergvelt

Research output: Contribution to journalArticlepeer-review


We introduce hierarchies of difference equations (referred to as nT-systems) associated to the action of a (centrally extended, completed) infinite matrix group GL∞(n) on n-component fermionic Fock space. The solutions are given by matrix elements (I"-functions) for this action. We show that the I"-functions of type nT satisfy bilinear equations of length 3, 4,...,n + 1. The 2T-system is, after a change of variables, the usual 3 term T-system of type A. Restriction from GL∞(n) to a subgroup isomorphic to the loop group LGLn, defines nQ-systems, studied earlier in [1] by the present authors for n = 2, 3.

Original languageEnglish (US)
Article number1850090
JournalInternational Journal of Mathematics
Issue number13
StatePublished - Dec 1 2018


  • Discrete integrable systems
  • Gauss factorizations
  • Q - and T -systems
  • tau-functions

ASJC Scopus subject areas

  • Mathematics(all)

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