Harish-Chandra’s homomorphism, Verma modules

نویسنده

  • Paul Garrett
چکیده

The Harish-Chandra homomorphism is due to [Harish-Chandra 1951]. Attention to universal modules with highest weights is in ]Harish-Chandra 1951], [Cartier 1955], as well as [Verma 1968], [BernsteinGelfand-Gelfand 1971a], [Bernstein-Gelfand-Gelfand 1971b], [Bernstein-Gelfand-Gelfand 1975]. See also [Jantzen 1979]. [1] We treat sl(2) in as simple a style as possible, to highlight ideas. Then sl(3) to illustrate that certain technical complications are harmless. One should be aware that some properties hold for sl(3) that become more complicated or fail completely for sl(4) and larger algebras. See the Supplementary Remarks to chapter 7 of [Dixmier 1977].

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تاریخ انتشار 2017