TY - JOUR

T1 - Difference Hierarchies for n T I" -functions

AU - Addabbo, Darlayne

AU - Bergvelt, Maarten

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Discrete integrable systems

KW - Gauss factorizations

KW - Q - and T -systems

KW - tau-functions

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U2 - 10.1142/S0129167X18500908

DO - 10.1142/S0129167X18500908

M3 - Article

AN - SCOPUS:85058228755

VL - 29

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 13

M1 - 1850090

ER -