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, Lectures by Joseph Bernstein. Written by Karl E. Rumelhart, Harvard University, http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/Bernst_Lecture_p-adic_repr.pdf 
• Bernšteĭn, I. N.; Zelevinskiĭ, A. V. (1976), "Representations of the group GL(n,F), where F is a local non-Archimedean field", Akademiya Nauk SSSR I Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk, Translation in Russian mathematical Surveys 31 (3): 5–70, ISSN 0042-1316, http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/B-Zel-RepsGL-Usp.pdf 
• 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, http://www.numdam.org/item?id=ASENS_1977_4_10_4_441_0 
• 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, http://www.numdam.org/item?id=ASENS_1980_4_13_2_165_0