Refine search
Actions for selected content:
1 results
Restriction problem for mod p representations of GL2 over a finite field
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 69 / Issue 3 / September 2026
- Published online by Cambridge University Press:
- 07 January 2026, pp. 1054-1067
- Print publication:
- September 2026
-
- Article
-
- You have access
- HTML
- Export citation
-
Let ${\mathbb {F}_q}$
be the finite field with $q = p^f$
elements. We study the restriction of two classes of mod p representations of ${G_q} = \text {GL}_2({{\mathbb {F}_q}})$
to ${G_p} = \text {GL}_2({\mathbb {F}_p})$
. We first study the restrictions of principal series which are obtained by induction from a Borel subgroup ${B_q}$
. We then analyze the restrictions of inductions from an anisotropic torus ${T_q}$
which are related to cuspidal representations. Complete decompositions are given in both cases according to the parity of f. The proofs depend on writing down explicit orbit decompositions of ${G_p} \backslash {G_q} / H,$
where $H = {B_q}$
or ${T_q}$
using the fact that ${G_q}/H$
is an explicit orbit in a certain projective line, along with Mackey theory.
