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Cartan–Gram determinants for the simple Lie groups
dc.contributor.authorWu, Alfred C. T.en_US
dc.date.accessioned2010-05-06T21:29:44Z
dc.date.available2010-05-06T21:29:44Z
dc.date.issued1982-11en_US
dc.identifier.citationWu, Alfred C. T. (1982). "Cartan–Gram determinants for the simple Lie groups." Journal of Mathematical Physics 23(11): 2019-2021. <http://hdl.handle.net/2027.42/70011>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70011
dc.description.abstractThe Cartan–Gram determinants for the simple root systems are evaluated for the simple Lie groups An, Bn, Cn, Dn, and Ek (k=6,7,8). The determinants satisfy a linear recursion relation which turns out to be the same for all these groups. For the En family, the Cartan–Gram determinant contains an explicit factor of (9−n) which vanishes for n=9 and is negative for n>9. This gives a simple explanation why the En family terminates at E8. The Cartan–Gram determinant affords a systematic explanation for the nonexistence of the forbidden Dynkin diagrams.en_US
dc.format.extent3102 bytes
dc.format.extent118344 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleCartan–Gram determinants for the simple Lie groupsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70011/2/JMAPAQ-23-11-2019-1.pdf
dc.identifier.doi10.1063/1.525257en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceE. B. Dynkin, Usp. Mat. Nauk. 2, No. 4 (20), 59 (1947); Transl. Am. Math. Soc. 9, 328 (1962).en_US
dc.identifier.citedreferenceN. Jacobson, Lie Algebras (Wiley, New York, 1962).en_US
dc.identifier.citedreferenceR. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications (Wiley, New York, 1974).en_US
dc.identifier.citedreferenceB. G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974).en_US
dc.identifier.citedreferenceR. Slansky, “Group Theory for Unified Model Building,” Phys. Rep. 79, 1 (1981).en_US
dc.identifier.citedreferenceA. O. Barut and R. Raczka, Theory of Group Representations & Applications (PWN Scientific Publishers, Warsaw, 1980), 2nd rev. ed.en_US
dc.identifier.citedreferenceSee, e.g., R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley‐Interscience, New York, 1953), Vol. 1, p. 34.en_US
dc.owningcollnamePhysics, Department of


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