有扭仿射李代数赋值模的某些性质

On some properties of evaluation modules for twisted affine Lie algebras

设g为有限维复单李代数,■[σ]为对应的有扭仿射李代数,U1,…,Ur为不可约g-模,z1,…,zr为互不相同的非零复数.利用生成函数的方法证明赋值模U1(z1)…Ur(zr)为■[σ]-模范畴E中不可约模并证明其同构定理.

Let be a simple finite-dimensional Lie algebra, g^^[ σ ] be the corresponding twisted affine Lie algebra, Uj（j = 1,…r, ） be finite-dimensional irreducible g-modules,and zj（j = 1,…r） be distinct nonzero complex numbers.In this paper,using the method of generating functions,we prove that the evaluation module U1 （z1）×…×Ur （Zr ）is irreducible in the category E of g^^[σ] - and we verify the isomorphism theorem.