Maarten Bergvelt

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Jan
16
comment From Sato grassmannian to spectral curve
The Kontsevich-Witten tau funtion is in fact a solution of the Kortewg-de Vries hierarchy, not just of KP. This means that the corresponding point of the Grassmannian comes from an element Of the loopgroup of Sl_2, not from an element of the general linear group. Such points always have z^2 as stabilizer, so for trivial reasons we get a P^1 as spectral curve. The "honest" spectral curves for KdV are 2-fold covers of this base curve. See, as always, Segal-Wilson.
Jan
15
comment From Sato grassmannian to spectral curve
Well, look for all g such that $g\phi_k$ is a linear combination of the basis elements. You get a bunch of equations for the coefficients of g. Yes, it is an interesting exercise to see if the Kontsevich-Witten point has a spctral curve. I do not know the answer, but you would expect that the curve would be trivial, no? It would be very strange if the genus of this curve would be any finite number. I am not sure if you can get infinite genus curves in this way.
Jan
14
awarded  Teacher
Jan
14
comment From Sato grassmannian to spectral curve
I am not sure what your notation means. Is \phi_k a basis for the point of the Grassmannian? In any case, for a generic point of the Grassmanian the spectral curve will be trivial.
Jan
14
answered From Sato grassmannian to spectral curve