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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Generalized spin representations - Guntram Hainke
(Birmingham)
DTSTART;TZID=Europe/London:20110309T163000
DTEND;TZID=Europe/London:20110309T173000
UID:TALK29722AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29722
DESCRIPTION:The special orthogonal group SO(n\,R) is a maximal
compact subgroup of SL(n\,R).\nIts Lie algebra th
erefore is called a maximal compact subalgebra of
sl(n\,R)\,\nand it can be characterized as the fi
xed point set of the Cartan-Chevalley involution s
ending a matrix to minus its transpose.\nKac-Moody
algebras were introduced in the 1960's to general
ise complex semisimple Lie algebras and have since
then found applications in theoretical physics. F
or\na Kac-Moody algebra one can similarly define
its maximal compact subalgebra as the fixed points
of the involution.\nIn the case of E(10)\, theore
tical physicists have discovered that the spin rep
resentation of so(10) can be extended to a represe
ntation of the maximal compact subalgebra of E(10)
.\nIn this talk\, we discuss this representation a
nd introduce a general framework which\nencompasse
s it. With the help of these so-called generalized
spin representations\,\nwe derive some algebraic
properties of maximal compact subalgebras of simpl
y-laced\nKac-Moody algebras.\nThis is joint work w
ith Ralf Gramlich.
LOCATION:MR15
CONTACT:Christopher Brookes
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