TY - JOUR
T1 - Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians
Y1 - 2014
A1 - Ferenc Balogh
A1 - Tiago Fonseca
A1 - John P. Harnad
AB - We study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function.
PB - American Institute of Physics Inc.
UR - http://urania.sissa.it/xmlui/handle/1963/34952
U1 - 35153
U2 - Mathematics
U4 - 1
ER -