多重Loop李代数的Weyl模

Weyl Modules for the Iterated Loop Algebras

设g为任意有限维复单李代数及Aν=C[t1±1,…,tν±]为ν个交换变量的Laurent多项式环.令L(g)=g C[t1±1,…,tν±]为多重Loop李代数.考虑L(g)上的Weyl模,证明了这类模都是有限维的,并且在适当的条件下证明了由一个元素生成的多重Loop代数的模一定是Weyl模的同态像.最后给出了Weyl模的一个张量积分解.

Let g be any finite-dimensional simple Lie algebra over the complex field C and Aν=C[t±11,…,t±1ν] be the Laurent polynomial ring in ν commutating variables.Let L（g）=g C[t±11,…,t±1ν] be an iterated loop algebra.We consider the Weyl modules over L（g）.We prove that the Weyl modules are finite-dimensional and any module under some assumption is a quotient of such a module.Finally,we give a tensor product decomposition for the Weyl modules.