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DTSTART:20180325T030000
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DTSTAMP:20191120T072943Z
UID:5936c170430d2148702062@ist.ac.at
DTSTART:20180426T130000
DTEND:20180426T150000
DESCRIPTION:Speaker: Christoph Geiss\nhosted by Tamas Hausel\nAbstract: Thi
s is a report on an ongoing project with B. Leclerc and J. Schroeer. Our a
im is to extend Lusztig's constructionof a semicanonical basis for the env
eloping algebra of the positive part of a symmetric Kac-Moody Lie algebra\
,which is in terms of the preprojective algebra of the corresponding quive
r over the complex numbers\, to the morenatural case of symmetrizable Kac-
Moody Lie algebras. To this end we study certain quivers\, which usually c
ontainloops\, together with a potential and some nilpotency conditions. Mo
st of the basic constructions carry over to thisnew setup with some modifi
cations. In particular\, the components of maximal dimension of our genera
lized nilpotentvarieties have the structure of a B(\\infty)-crystal of the
corresponding type\, and we can construct semicanonical functions associa
ted to those components. To conclude\, we would have to show that the cons
tructible functionswhich have support with positive codimension\, form an
ideal.In the second part we can give some more details about the proofs an
d discuss the case B_2\, which supports ourconjecture.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
T Austria
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Quivers with relations for symmetrizable Cartan matrices and semica
nonical functions
URL:https://talks-calendar.app.ist.ac.at/events/1207
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