Representations of finite groups of Lie type
Representations of finite groups of Lie type
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DOI：
10.1090/s0273-0979-1979-14648-2
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发表时间：
1979-09
影响因子：
1.3
通讯作者：
C. Curtis
中科院分区：
文献类型：
--
作者：
C. Curtis
群G在复数域上的表示理论涉及两个问题：第一，G的不可约表示的构造；第二，用不可约表示的系数的线性组合（或线性组合的极限）来表示G上每一个适当限制的复值函数的问题。例如，如果G是实数的可积群对1（一维环面）取模，我们考虑G上的可积函数，或者是同样的，实数的可积群上周期为1的可积周期函数。在这种情况下，G的不可约表示由指数函数x - e给出，其中k是整数，并且是G到复数相乘群的连续同态。不可约表示{e}的可积函数的表达式是/的傅里叶展开式，
The representation theory of a group G over the field of complex numbers involves two problems: first, the construction of the irreducible representations of G; and second, the problem of expressing each suitably restricted complex valued function on G, as a linear combination (or a limit of linear combinations), of the coefficients of the irreducible representations. For example, if G is the additive group of real numbers mod 1 (the one-dimensional torus), one considers integrable functions on G, or what is the same thing, integrable periodic functions of period 1 on the additive group of real numbers. In this case the irreducible representations of G are given by the exponential functions x -» e, where k is an integer, and are the continuous homomorphisms from G into the multiplicative group of complex numbers. The expression of an integrable function in terms of the irreducible representations {e} is the Fourier expansion of/,