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| POINTED REPRESENTATIONS OF INFINITE DIMENSIONAL LIE ALGEBRAS |
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Citation： |
Xu Xiang.POINTED REPRESENTATIONS OF INFINITE DIMENSIONAL LIE ALGEBRAS[J].Chinese Annals of Mathematics B,1995,16(2):255~260 |
| Page view： 933
Net amount： 591 |
Authors： |
Xu Xiang; |
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| Abstract： |
A contravariant bilinear pairing $K$ on every
$M(\rho)\times M(\rho \theta)$ is determined and it is proved that $M(\rho)$ is
irreducible if
and only if $K$ is left nondegenerate. It is also proved that every cyclic
pointed module is a quotient of some Verma-like pointed module;
moreover if it is irreducible then it is a quotient of the
Verma-like pointed module by the left
kernel of some bilinear pairing $K$. In case the mass function is symmetric,
there exists a bilinear form on $M(\rho)$. It is proved that unitary pointed
modules are integrable. In addition, a characterization of the mass functions of
Kac-Moody algebras is given, which is a generalization of the finite
dimensional Lie algebras case. |
Keywords： |
Pointed representation, Primitive cycle, Mass function,Bilinear pairing. |
Classification： |
17B65 |
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