# The characters of semisimple Lie groups

@article{HarishChandra1956TheCO, title={The characters of semisimple Lie groups}, author={Harish-Chandra}, journal={Transactions of the American Mathematical Society}, year={1956}, volume={83}, pages={98-163} }

is of the trace class and the mapping Tr:f—*sp(ir(f)) is a distribution on G which is called the character of ir (see [6(d)]). In this paper we shall obtain some results on these characters. Let / be the rank of G. We say that an element xEG is regular if / is exactly the multiplicity of the eigenvalue 1 of the matrix which corresponds to x in the adjoint representation of G. The regular elements form an open and dense subset G' of G. We shall prove (Theorem 6) that TT coincides on G' (in the…

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