仿射李代数上基本模的极大权

The Maximum Weights of Fundamental Module Over Affine Lie Algebras

设g(A)是结合于仿射型广义Cartan矩阵A的Kac-Moody代数,L(Λ)(Λ∈P+)是g(A)上可积不可约的最高权模。文献[1]证明了L(Λ)的支配极大权只有有限个,并且决定了A^((k))_l,D^((k))_l,E^((k))_l(k=1,2,3)型Kac-Moody代数上水平1的可积不可约模L(Λ)的极大权集及权系。本文试图用不同于[1]的方法,也是更直接的方法,来决定C^((1))_2,G^((1))_2型Kac-Moody代数上基本不可约模L(Λ)的极大权集和权系。 本文所使用的术语和记号均见文献[1]。

Let g(A) be the Kac-Moody algebra associated to a generalized Cartan matrix A of affine type, L(f2)(Λ∈P+) be an irreducible highest weight module over s(A). Literature proved that the number of dominate maximum weights of L(Λ) is finite, and determined the set of maximum weights and weight system of L(Λ) of level one over the Kac-Moody algebra of types Al(k), Dl(k), -El(k)(k = 1,2 ,3). In this paper a different method, a more direct method is used to determine the set of maximum weights and weight system of fundamental module L(Λ) over C2(1), G2(1).