关于Dn型外尔群的本原幂等元

On the primitive idempotents of the Weyl group of type D

设n≥4是自然数,W(Dn)是Dn型的有限外尔群,设K是一个域且群代数K[W(Dn)]在域K上分裂半单.对于K[W(Dn)]的每一个单模U,精确构造了一个拟幂等元zU ∈K[W(Dn)],即存在cU∈K×,有zU2=cUzU,使得cU-1 zU为本原幂等元,并且zUK[W(Dn)]作为右K[W(Dn)]-模同构于U.主要研究结果推广了 Dipper、James关于A型及B型外尔群半单群代数的本原幂等元的构造.

Let 4≤n∈N and W(Dn) the Weyl group of Type Dn.Let K be a field and group algebra K[W(Dn)] is split semisimple on the field K.for each simple module U of K[W(Dn)],we explicitly construct a quasi-idempotent zU ∈ K[W(Dn)](i.e.,zU2=cUzU for some cU∈K× such that cU-1zU is a primitive idempotent and zUK[W(Dn)]■U as a right K[W(Dn)]-module.The main results of this paper generalize the construction of primitive idempotents by Dipper and James on semi-simple group algebras of type A and B Weyl groups.