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Robert Langlands on Harish-Chandra [2014]

Harish-Chandra---IISER Pune There are at several aspects of Harish-Chandra, his life, and his work on which one can reflect: his personality; the nature of his contributions and their position in mathematics; his relation to the land of his birth. It would have been in 1961-62, as I was beginning to reflect on the trace formula of Selberg and, in particular, attempting to evaluate the integrals that arise when using it to calculate the dimension of the space of automorphic forms, that David Lowdenslager, a young mathematician at Princeton University who not long afterwards met an unfortunate accidental death, suggested to me that it was becoming accepted that the papers of Harish-Chandra, who had begun his prolific career just a few years before, might be pertinent. Among other things his first papers on the holomorphic discrete series had already appeared. I began to read them and to reflect. It did not take long until one day, on the brief walk home from the mathematics department at Princeton University---the spot is still there, not yet buried under still another building, or still more asphalt paving---I recognized that the integral with which I was attempting to deal was an orbital integral of a matrix coefficient of a representation in the holomorphic discrete series and therefore, according to a theory familiar for finite groups from the time of Frobenius, given by the value of a character. http://publications.ias.edu/rpl/paper...