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DTSTART:20230326T030000
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BEGIN:VEVENT
DTSTAMP:20240806T022737Z
UID:1683802800@ist.ac.at
DTSTART:20230511T130000
DTEND:20230511T150000
DESCRIPTION:Speaker: Oksana Yakimova\nhosted by Tamas Hausel\nAbstract: Let
g be a complex reductive Lie algebra. The algebra S(g)^g of symmetric
g-invariants and the centre Z(g) of the enveloping algebra U(g) are poly
nomial rings in the rank of g generators. There are several isomorphism
s between these rings\, including the symmetrisation map\, which exists al
so for the inline-dimensional Lie algebras. However\, in case of an infini
te-dimensional Lie algebra q\, one may need to complete U(q) in order to r
eplace Z(q) with an interesting related object. Roughly speaking\, the Fei
gin--Frenkel centre arises as a result of such completion in case of an a
ffine Kac--Moody algebra. From 1982 until 2006\, this algebra existed as a
n intriguing black box with many applications. Then explicit formulas for
its elements appeared first in type A\, later in all other classical typ
es\, and it was discovered that the FF-centre is the centraliser of the qu
adratic Casimir element. We will discuss the type-free role of the symmet
risation map in the description of the FF-centre and present new explicit
formulas for its generators in types B\, C\, D\, and G_2.
LOCATION:Heinzel Seminar Room (I21.EG.101)\, Office Building West\, ISTA\,
ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Oksana Yakimova: Symmetrisation and the Feigin--Frenkel centre
URL:https://talks-calendar.ista.ac.at/events/4135
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