Is there an analogue of [1, Thm. 10.23] for ordinary smooth representations of a locally profinite group (l.p.g. for short)?
I have already checked introductory chapters of some classical references in ordinary smooth representation theory of l.p.g.'s [2, 3, 4] but without success.
The closest hint I was given seems to be the general discussion in [5, Sec. 5.5], but unfortunately I cannot access it freely on the Internet or in any library from my university. Thank you in advance.
Bibliography
[1] C. W. CURTIS AND I. REINER, Representation Theory of Finite Groups and Associative Algebras, John Wiley and Sons Inc, 1962.
[2] C. J. BUSHNELL AND G. HENNIART, The Local Langlands Conjecture for GL(2), Springer, 2006.
[3] W. CASSELMAN, Introduction to the theory of admissible representations of p-adic reductive groups (1974), Preprint, University of British Columbia.
[4] I.N. BERNSTEIN AND A.V. ZELEVINSKY, Representations of the group GL(n, F) where F is a local non-archimedean field, Uspekhi Mat. Nauk 31 (1976), 5–70.
[5] M.-F. VIGNÉRAS, Représentations l-modulaires d'un groupe réductif p-adique avec l $\neq$ p, Progress in Math. 137, Birkhaüser, 1996.