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The work of Robert Langlands

Representation theory

Dimension of spaces of automorphic forms

This first appeared in the Proceedings of the AMS Symposium at Boulder, Colorado, held in the summer of 1965.

Langlands' comments:

    Although the principal purpose of this paper was to review how the Selberg trace formula is combined with character formulas to calculate the dimension of various spaces of automorphic forms. it is included as a paper on representation theory because the most influential observation in the paper was the description of a possible realization of the discrete series representations on spaces of L2-cohomology.

The classification of representations of real reductive groups

This was written in 1973. It first appeared as a preprint distributed by the Institute for Advanced Study, and was later (1988) published by the A.M.S. in Math. Surveys and Monographs 31.

Langlands' comments:

Notes on Knapp-Zuckerman theory

This has not been published before. It was written around 1977, just after A. Knapp and G. Zuckerman had announced their results on reducible unitary principal series, subsequently explained in a talk at the A.M.S. 1977 summer school in Corvallis (pp. 93-105 of the published proceedings of that conference.)

On unitary representations of the Virasoro algebra

First appeared in Infinite-dimensional Lie algebras and their applications, World Scientific, 1988.

The factorization of a polynomial defined by partitions

First appeared in Commun. Math. Phys. 124 (1989).