Bernstein–Zelevinsky classification

In mathematics, the Bernstein–Zelevinsky classification, introduced by Bernstein and Zelevinsky (1977) and Zelevinsky (1980), classifies the irreducible complex smooth representations of a general linear group over a local field in terms of cuspidal representations.

References

• Bernstein, J. (1992), Representations of p-adic groups (PDF), Lectures by Joseph Bernstein. Written by Karl E. Rumelhart, Harvard University
• Bernšteĭn, I. N.; Zelevinskiĭ, A. V. (1976), "Representations of the group GL(n,F), where F is a local non-Archimedean field" (PDF), Akademiya Nauk SSSR I Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk, Translation in Russian mathematical Surveys, 31 (3): 5–70, ISSN 0042-1316, MR 0425030
• Bernstein, I. N.; Zelevinsky, A. V. (1977), "Induced representations of reductive p-adic groups. I", Annales Scientifiques de l'École Normale Supérieure, Série 4, 10 (4): 441–472, doi:10.24033/asens.1333, ISSN 0012-9593, MR 0579172
• Zelevinsky, A. V. (1980), "Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n)", Annales Scientifiques de l'École Normale Supérieure, Série 4, 13 (2): 165–210, doi:10.24033/asens.1379, ISSN 0012-9593, MR 0584084