The characters of semisimple Lie groups

  title={The characters of semisimple Lie groups},
  journal={Transactions of the American Mathematical Society},
  • Harish-Chandra
  • Published 1956
  • Mathematics
  • Transactions of the American Mathematical Society
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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  • Harish-Chandra
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1957
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