LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that ...LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).展开更多
In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-dens...In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.展开更多
基金supported by the Natural Science Foundation of USA (Grant No. DMS 0701578)supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Gttingen
文摘LetG = SLn(C)Cn be the (special) affine group. In this paper we study the representation theory of G and in particular the question of rationality for V/G, where V is a generically free G-representation. We show that the answer to this question is positive (Theorem 6.1) if the dimension of V is sufficiently large and V is indecomposable. We explicitly characterize two-step extensions 0 → S → V → Q → 0, with completely reducible S and Q, whose rationality cannot be obtained by the methods presented here (Theorem 5.3).
基金Project supported by the Tianyuan Foundation of Mathematics (No. A0324624)the National Natural Science Founcation of China (No. 10371040)the Shanghai Priority Academic Discipline.
文摘In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.
