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SUMMARY:Georgy Sharygin: Full symmetric Toda flows on real Lie groups and
Bruhat order
DTSTART;VALUE=DATE-TIME:20200129T151500Z
DTEND;VALUE=DATE-TIME:20200129T161500Z
DTSTAMP;VALUE=DATE-TIME:20200410T000330Z
UID:indico-event-5506@indico.math.cnrs.fr
DESCRIPTION:The full symmetric Toda system is a straightforward generaliza
tion of the usual (3-diagonal) system\; it can be further generalized to t
he case of Cartan decomposition of an arbitrary real semisimple Lie group.
In this case the integrability of the system is known\, but the construct
ions of the involute families of integrals are usually quite complicated.
In my talk I will describe a construction of commutative family of vector
fields on the compact group\, analogous to the family of first integrals i
n involution. This construction is based on the structure of representatio
ns of the original group. If time permits\, I will also describe the relat
ion of this construction with Sorin and Chernyakovâ€™s and Reshetikhin and
Schraderâ€™s constructions\, proving the noncommutative integrability of
the system. If time permits\, I shall also speak about another interesting
aspect of the full symmetric Toda system: it turns out\, that the phase p
ortrait of this system is determined by an important discrete structure\,
the so called Bruhat order on the Weyl group of the corresponding Lie grou
p. In my talk I will give the necessary definitions and sketch the proofs.
\n\nhttps://indico.math.cnrs.fr/event/5506/
LOCATION: Salle A318
URL:https://indico.math.cnrs.fr/event/5506/
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