Discrete decomposability of restrictions of $$({mathfrak {g}},K)$$-modules for $$(G,G^sigma )$$ with an automorphism $$sigma $$ of even order
Discrete decomposability of restrictions of $$({mathfrak {g}},K)$$-modules for $$(G,G^sigma )$$ with an automorphism $$sigma $$ of even order
复制标题
$$({mathfrak {g}},K)$$-模的限制的离散可分解性，$$(G,G^sigma )$$ 具有偶数阶自同构 $$sigma $$
DOI：
10.1007/s10711-021-00657-4
复制
发表时间：
2021
影响因子：
0.5
通讯作者：
Haian He
中科院分区：
文献类型：
--
作者：
Haian He
设G是非紧连通单李群，G（sigma）是G上不动点在sigma作用下的子群，其中sigma是G的偶数阶自同构.本文给出了对（G，G（sigma））满足条件（D.D.）的一个必要条件;也就是说，至少存在一个无限维的简单（g，K）-模，它可以离散地分解为（g（sigma），K-sigma）-模。
Let G be a noncompact connected simple Lie group, and G(sigma) the subgroup of the fixed points under the action of sigma on G, where sigma is an automorphism of G of even order. This article shows a necessary condition for the pair (G, G(sigma)) satisfying condition (D.D.); that is, there exists at lease one infinite-dimensional simple (g, K)-module that is discretely decomposable as a (g(sigma), K-sigma)-module.