Although much of the theory of finite-dimensional algebras had its origins in the theory of group representations, it seems simpler nowadays to develop the theory of algebras first and then use it to give an account of group representations. This theory has been a powerful tool in the study ...
第一个证明是存在性的,它通过Frobenius互反律,连接了酉空间的许多性质,这是一个非常有用的观点。第二个证明是构造性的,它直接构造出了对应表示,注意,这里的证明可以说是下一章命题18的特殊情况,即p不能整除群G的阶的情况,此时p初等子群都是循环群,从这个观点看,Artin定理又是这个命题的特例。 第三题也比较重...
First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics...
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module...
We prove an analogue of the celebrated Hall-Higman theorem, which gives a lower bound for the degree of the minimal polynomial of any semisimple element of prime power order $p^{a}$ of a finite classical group in any nontrivial irreducible cross characteristic representation. With a few expli...
This chapter discusses the representation theory of finite groups. Every irreducible representation of a group G occurs as an irreducible constituent of the regular representation. The number of irreducible representations of G is the same as the number of principal indecomposable representations. The ...
2) Representation theory of finite group 有限群表示论3) finite group 有限群 1. Directed subgroup graph for studying the subgroup properties of finite groups; 利用有向子群图研究有限群的子群性质 2. On the solvability of finite groups based on normal indexes; 有限群可解性的正规指数刻画 3....
The main intersting thing in Representation Theory is to study agroupGas a group of matrices. First we defineFG-modules, group algebra ,FG-Homomorphism. Then there is a big result namely Maschke's Theorem, this tellsthat for a finite groupG, ifUbe theFG-submodule of the FG-module then ...
群与图 Graphs and Groups 有限群 Finite Groups 有限置换群 Finite Permutation Group ... www.combinatorics.net.cn|基于14个网页 2. 有限群结构 研究生教育-培养园地... ... 复几何 Complex Geometry 有限群结构 Finite Groups 群表示论 Representation Theory of Groups ... math.sysu.edu.cn|基于2个网页...
This paper advocates a new approach in the theory of finite group representations by applying exclusively the method of commuting operators in quantum mechanics. The basic problems of group representation theory, such as the labeling of the irreducible representations, the calculation of characters, irre...