arXiv subjects

François Courtès

Publications and source records attributed to François Courtès.

3 recordsLinked to original sources

arXiv2016

Distinction of the Steinberg representation III: the tamely ramified case

Let $F$ be a nonarchimedean local field, let $E$ be a Galois quadratic extension of $F$ and let $G$ be a quasisplit group defined over $F$; a conjecture by Dipendra Prasad states that the Steinberg representation of $G(E)$ is then $χ$-distinguished for a given unique character $χ$ of $G(F)$. In the first two papers of the series, Broussous and the author have proved that result when $G$ is $F$-split and $E/F$ is unramified; this paper deals with the tamely ramified case, still with $G$ $F$-split.

math.RT↗

arXiv2015

A characterization of groups of parahoric type

Let F be a local henselian nonarchimedean field of residual field k, and let G be the group of F-points of a connected reductive group defined over F. It is well-known that the quotient of any parahoric subgroup of G by its first congruence subgroup is isomorphic to the group of k-points of a reductive group defined over k, and conversely; in this paper, we generalize this result by studying a class of linear algebraic groups named groups of parahoric type; we prove that, under certain conditions, any such group is k-isomorphic to the quotient of a parahoric subgroup of some reductive group over F by its h-th congruence subgroup for a suitable h.

math.GR↗

arXiv2011

Steinberg representations for groups of parahoric types: the special case

In this paper, we define and study a kind of Steinberg representation for linear algebraic groups of a particular kind, called groups of parahoric type, defined overa finite field; in particular, when G is the group of F-points of a connected reductive quasisplit group defined over F which splits over an unramified extension of F, the quotients of parahoric subgroups of G by their congruence subgroups are groups of parahoric type. In particular, under certain conditions on the residual characteristic p of F, we determine the irreducible factors of the Steinberg representation of a group of parahoric type associated to a pseudo-Borel subgroup of this group in the special case, that is when this group os a quotient of a maximal special parahoric subgroup of G.

math.GR↗