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. 

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.