Weyl代数的表示

Representations of Weyl Algebras

英文关键词:n-th weylalgebra A_ｎ（k）  irreducible modules  Harcsh- Chandra modules  finite dimensional representation.

中文摘要:

      设Ｋ是一个域．证明了，若ｃｈＫ＝０，那么ｎ－ｔｈＷｅｙｌ代数Ａ_ｎ（ｋ）没有有限维表示．还给出了Ａ_ｎ（ｋ）的不可约Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模的分类．当Ｋ是一个特征非零的代数闭域时，给出了有限维不可约Ａ_ｎ（Ｋ）－模的分类．

英文摘要:

      Let K be a field. In this paper, we proved that if ch K =0 ,then the n-thWeyl algebra A_ｎ(K) has no finite dimensional representation . And the classification of irreducible (and indecomposable) Harish-Chandra modules over the n-th Weyl algebra A_ｎ(K) is given. If K is all algebraically closed field of characteristic ≠0, then the classification of finite dimensional irreducible A_ｎ(K)-modules is got.