We study, by means of Littelmann's theory of paths, Kostant-Kumar modules (KK modules for short), which by definition are certain submodules of the tensor product of two irreducible integrable highest weight representations of a symmetrizable Kac-Moody algebra. Our main result is an identification of a path model for any KK module as a subset of the well known path model for the tensor product consisting of concatenations of Lakshmibai-Seshadri paths. The technical results about extremal elements in Coxeter groups that we formulate and prove en route and the technique of their proofs should be of independent interest. We also discuss the existence of PRV components and generalised PRV components in KK modules.

我们通过利特尔曼的路径理论研究Kostant-Kumar模块（简称KK模块），根据定义，它们是对称Kac-Moody代数的两个不可约可积最高权表示的张量积的某些子模块。我们的主要结果是，将任何KK模块的路径模型标识为张量积的已知路径模型的子集，该张量积由Lakshmibai-Seshadri路径的串联组成。我们在旅途中制定和证明的有关Coxeter组中极值元素的技术结果以及它们的证明技术应该是相互独立的。我们还将讨论KK模块中PRV组件和广义PRV组件的存在。