Topology of the Real Part of the Hyperelliptic Jacobian Associated with the Periodic Toda Lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 439-462
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We study the topology of the isospectral real manifold of the ${\mathfrak sl}(N)$ periodic Toda lattice consisting of $2^{N-1}$ different systems. The solutions of these systems contain blow-ups, and the set of these singular points defines a divisor of the manifold. With the divisor added, the manifold is compactified as the real part of the $(N-1)$-dimensional Jacobi variety associated with a hyperelliptic Riemann surface of genus $g=N-1$. We also study the real structure of the divisor and provide conjectures on the topology of the affine part of the real Jacobian and on the gluing rule over the divisor to compactify the manifold based on the sign representation of the Weyl group of ${\mathfrak sl}(N)$.
Keywords:
periodic Toda lattice, Jacobian variety, theta divisor, Riemann theta function.
@article{TMF_2002_133_3_a9,
author = {Y. Kodama},
title = {Topology of the {Real} {Part} of the {Hyperelliptic} {Jacobian} {Associated} with the {Periodic} {Toda} {Lattice}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {439--462},
publisher = {mathdoc},
volume = {133},
number = {3},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a9/}
}
TY - JOUR AU - Y. Kodama TI - Topology of the Real Part of the Hyperelliptic Jacobian Associated with the Periodic Toda Lattice JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2002 SP - 439 EP - 462 VL - 133 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a9/ LA - ru ID - TMF_2002_133_3_a9 ER -
Y. Kodama. Topology of the Real Part of the Hyperelliptic Jacobian Associated with the Periodic Toda Lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 439-462. http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a9/