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TZID:Europe/Vienna
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DTSTART:20190331T030000
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DTSTART:20191027T020000
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BEGIN:VEVENT
DTSTAMP:20210515T021609Z
UID:5c3337d55e1a3007748319@ist.ac.at
DTSTART:20190919T133000
DTEND:20190919T153000
DESCRIPTION:Speaker: Alice B. Tumpach\nhosted by Tamas Hausel\nAbstract: Th
e aim of this talk is to give an interpretation in terms of Poisson geomet
ry of the algebro-geometric solutions of the Korteweg-de-Vries hierarchy c
onstructed by Segal and Wilson in 1985. The central object in this theory
is the restricted Grassmannian\, which is an homogeneous Ka ?hler Hilbert
manifold. We construct a generalized Banach Poisson-Lie group structure on
the unitary restricted group\, as well as on a Banach Lie group consistin
g of (a class of) upper triangular bounded operators. We show that the res
tricted Grassmannian inherites a Bruhat-Poisson structure from the unitary
restricted group. Furthermore the action of the triangular Banach Lie gro
up on it by dressing transformations generates the KdV hierarchy (as was p
ointed out by Segal and Wilson)\, and its orbits are the Schubert cells of
the restricted Grassmannian.
LOCATION:Heinzel Seminar Room / Office Bldg West (I21.EG.101)\, IST Austria
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Bruhat-Poisson structure of the restricted Grassmannian and the KdV
hierarchy
URL:https://talks-calendar.app.ist.ac.at/events/2156
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