Projects per year
Abstract
Let o be the ring of integers in a nonArchimedean local field with finite residue field, p its maximal ideal, and r ≥ 2 an integer. An irreducible
representation of the finite group G_{r} = GL_{N} (o/p
^{r}
), for an integer N ≥ 2,
is called regular if its restriction to the principal congruence kernel K^{r−1} =
1 + p^{r}−1 M_{N} (o/p^{r}
) consists of representations whose stabilisers modulo K^{1}
are centralisers of regular elements in M_{N} (o/p).
The regular representations form the largest class of representations of G_{r} which is currently amenable to explicit construction. Their study, motivated by constructions of supercuspidal representations, goes back to Shintani, but the general case remained open for a long time. In this paper we give an explicit construction of all the regular representations of G_{r}.
The regular representations form the largest class of representations of G_{r} which is currently amenable to explicit construction. Their study, motivated by constructions of supercuspidal representations, goes back to Shintani, but the general case remained open for a long time. In this paper we give an explicit construction of all the regular representations of G_{r}.
Original language  English 

Pages (fromto)  1066–1084 
Number of pages  29 
Journal  Bulletin of the London Mathematical Society 
Volume  49 
Issue number  6 
Early online date  19 Oct 2017 
DOIs  
Publication status  Published  Dec 2017 
Profiles

Shaun Stevens
 School of Mathematics  Professor of Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research
Projects
 1 Finished

Explicit Correspondences in Number Theory.
Engineering and Physical Sciences Research Council
31/03/10 → 30/03/15
Project: Fellowship