## A q-analogue of the Jantzen-Schaper theorem

### Gordon James and Andrew Mathas

#### Keywords

Hecke algebras, q-Schur algebras, Jantzen filtrations.

#### Status

* Proc. Lond. Math. Soc.*, **74** (1997), 241-274.

MR97j:20013

#### Abstract

In this paper we prove an analogue of Jantzen's sum formula for the
q-Weyl modules of the q-Schur algebra and, as a consequence,
derive the analogue of Schaper's theorem for the q-Specht modules of the
Hecke algebras of type **A**. We apply these results to classify the
irreducible q-Weyl modules and the irreducible (e-regular) q-Specht
modules, defined over any field. In turn, this
allows us to identify all of the ordinary irreducible representations of the
finite general linear group GL_{n}(q) which remain irreducible modulo a
prime p not dividing q.

*Andrew Mathas *

14th May 1996.