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SUMMARY:Generalized spin representations
DTSTART;VALUE=DATE-TIME:20130530T144500Z
DTEND;VALUE=DATE-TIME:20130530T154500Z
DTSTAMP;VALUE=DATE-TIME:20210417T123306Z
UID:indico-event-506@indico.math.cnrs.fr
DESCRIPTION:Motivated by the 32-dimensional extension of the spin represen
tation of the compact Lie algebra so(10) to the 'maximal compact' subalgeb
ra of the real Kac-Moody Lie algebra of type E10 described by Damour et al
. and Henneaux et al. Hainke and myself introduced the concept of a genera
lized spin representation that allows similar constructions for the 'maxim
al compact' subalgebras of real Kac-Moody Lie algebras of arbitrary simply
laced type. \n\nBy work of Ghatei\, Horn\, Weiss and myself\, integratio
n of these representations leads to two-fold spin covers of the 'maximal c
ompact' subgroups of the corresponding split real Kac-Moody groups. The pr
oblem that semisimple elements generally do not have a locally finite acti
on and therefore obstruct integration is circumvented by an amalgamation m
ethod using the Iwasawa decomposition and the theory of buildings. The exi
stence of these spin covers has been conjectured by Damour and Hillmann\;
it contains an extended Weyl group\, which in the E10 case is relevant to
fermionic billards.\n\nhttps://indico.math.cnrs.fr/event/506/
LOCATION:Institut des Hautes Etudes Scientifiques Amphithéâtre Léon Mot
chane
URL:https://indico.math.cnrs.fr/event/506/
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