某些A_l型Weyl模不可约的充要条件  

An Irreducible Condition of Certain Weyl Modules for Type A l

作　　者：蒋志洪[1] 陆金山 

机构地区：[1]上海铁道大学基础部,上海200331 [2]上海电器科学研究所,上海200063

出　　处：《上海铁道大学学报》1998年第3期94-98,共5页

摘　　要：在代数闭域ｋ的特征为零的条件下，通过对任意有限维Ｇ－模的ｎ次斜对称张量积和它的对偶模的ｍ次斜对称张量积的张量积研究，给出一个Ｇ－模满同态从∧ｎＭ∧ｍＭ＊到∧ｎ－１Ｍ∧ｍ－１Ｍ＊；然后在Ｇ＝ＳＬ（ｌ＋１，ｋ）时，证明了Ｖ（λａ）Ｖ（λｂ）ｍｉｎ（ａ，ｌ＋１－ｂ）ｉ＝０Ｖ（λａ－ｉ＋λｂ＋ｉ）。在代数闭域ｋ的特征为ｐ时。First, we assume that k is algebraically closed field of characteristic zero; M is G-module and dim M <∞. We consider that the tensor product of n times of the skew-symmetric tensor of m times of the skew-symmetric tensor M , and introduce an epimorphism from ∧ n M∧ m M  to ∧ n-1 M∧ m-1 M . Then we assume G=SL(l+1,k) we prove that V(λ a)V(λ b) min (a,l+1-b)i=0V(λ a-i +λ b+i ) Finally we assume the characteristic of k is p, and show that V(λ a+λ b) is irreducible module if and only if υ p[(b-a+i+1)/i]=0, (i=1,2,…,min(a,l+1-b))

关 键 词：不可约表示 WEYL模 张量积 线性代数群 

分 类 号：O152.6[理学—数学]