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SUMMARY:Generalized spin representations - Guntram Hainke (Birmingham)
DTSTART:20110309T163000Z
DTEND:20110309T173000Z
UID:TALK29722@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:The special orthogonal group SO(n\,R) is a maximal compact sub
 group of SL(n\,R).\nIts Lie algebra therefore is called a maximal compact 
 subalgebra of sl(n\,R)\,\nand it can be characterized as the fixed point 
 set of the Cartan-Chevalley involution sending a matrix to minus its trans
 pose.\nKac-Moody algebras were introduced in the 1960's to generalise comp
 lex semisimple Lie algebras and have since then found applications in theo
 retical physics. For\na Kac-Moody algebra one can similarly define its ma
 ximal compact subalgebra as the fixed points of the involution.\nIn the ca
 se of E(10)\, theoretical physicists have discovered that the spin represe
 ntation of so(10) can be extended to a representation of the maximal compa
 ct subalgebra of E(10).\nIn this talk\, we discuss this representation and
  introduce a general framework which\nencompasses it. With the help of the
 se so-called generalized spin representations\,\nwe derive some algebraic 
 properties of maximal compact subalgebras of simply-laced\nKac-Moody algeb
 ras.\nThis is joint work with Ralf Gramlich.
LOCATION:MR15
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