Induction and restriction of representations

在一个被称为李群表示论的纯数学领域，我对指数可解李群，其中指数映射是从李代数到李群的微分同态，进行了关于子群的一维么正特征标(单项表示)的诱导表示的不可约分解的研究，得到了以下结果1.如果一个单项表示在其不可约分解中的重数是离散型的，则我们可以显式地描述它的Plancerel公式，并证明相关的不变微分算子代数的交换性。我们还在Duflow的某个问题上发现了一个反例。收集到目前为止由Grants-in-Aid for Science Research获得的结果，我出版了一本研究书籍，名为《指数可解李群的酉表示》(Sugaku-Shobo，2010,352页)。

In a field of pure mathematics called representation theory of Lie groups, I carried out for exponential solvable Lie groups, where the exponential map is a diffeomorphism from Lie algebra onto Lie group, a research related to the irreducible decomposition of induced representation from a 1-dimensional unitary character of a subgroup (monomial representation) and obtained the following results.1. If the multiplicity of a monomial representation in its irreducible decomposition is of discrete type, we could describe explicitly its Plancherel formula and show the commutativity of the associated algebra of invariant differential operators. We also found a negative example on a certain problem of Duflo.2. Gathering the results obtained until now by Grants-in-Aid for Scientific Research, I published a research book entitled "Unitary representations of exponential solvable Lie groups"(Sugaku-shobo, 2010, 352 pages).