Titlebook: Representations of Compact Lie Groups; Theodor Bröcker,Tammo Dieck Textbook 1985 Springer Science+Business Media New York 1985 Groups.Lie.

auxiliary

Lie Groups and Lie Algebras,strates the notion of a Lie group with classical examples of matrix groups from linear algebra. The spinor groups are treated in a separate section, §6, but the presentation of the general theory of representations in this book presupposes no knowledge of spinor groups. They only appear as examples

precede

MUT

Representative Functions,The celebrated theorem of Peter and Weyl asserts that the representative functions are dense in the space of all continuous functions. This central result is proved in §3 with the help of some functional analysis which is reviewed in §2. We devote §1 to definitions and to showing that any (left or r

解决

Conquest

Root Systems, action of the Weyl group .. Characters are really functions on ./., and the Weyl integral formula transforms integrals of class functions on . into integrals of .-invariant functions on .. We therefore wish to investigate the structure of . as a .-manifold and of L. as a .-module. To do this we stu

哀求

Irreducible Characters and Weights, Lie group and the integral forms in a distinguished Weyl chamber. The character formula is stated and proved in the first section. In the second section we will introduce partial orderings on L.* and analyze the structure of the character ring. The third section gives us some efficient formulas for

试验

Lie Groups and Lie Algebras, structure of subgroups and quotients, and in §5 we explain how to construct an invariant integral using differential forms. We quote Stokes’ theorem to get a result about mapping degrees which we shall use in Chapter IV.

FATAL

The Maximal Torus of a Compact Lie Group, representation theory. In the third section we compute the maximal tori and Weyl groups of the classical Lie groups, and in the last section we give a generalization which handles the case of nonconnected groups.

Pigeon

抱狗不敢前