[ Main page on Langlands' work | Copyright notice ]

The work of Robert Langlands

Semi-groups and representation theory

Semi-groups and representations of Lie groups

This was submitted for a Ph.D. thesis in mathematics at Yale University.

Langlands' comments:

    There are two, related parts to this thesis: one on representations of Lie semi-groups and one on operators associated to representations of Lie groups. The first part was published in the Canadian Journal of Mathematics, but the second was published only as an announcement in the Proceedings of the National Academy of Sciences of the USA. It nevertheless had the good fortune to be taken seriously by Derek Robinson, who incorporated some of the results into his book on Elliptic Operators and Lie Groups.

    Examining again, after forty years, the verification of the basic estimates of the second part, I found a large number of misprints, so that it would have been difficult if not impossible to follow my arguments line by line. I have tried in the present version to correct the misprints, but cannot be certain to have fully succeeded.

    The thesis remains, to my regret, my only active encounter with partial differential equations, a subject to which I had always hoped to return but in a different vein.

Some holomorphic semi-groups

This first appeared in the the Proceedings of the National Academy of Sciences 46 (1960).

On Lie semi-groups

This first appeared in the Canadian Journal of Mathematics 12, 1960.