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Proceedings of the London Mathematical Society 1997 74(2):241-274; doi:10.1112/S0024611597000099
© 1997 by London Mathematical Society
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© London Mathematical Society

A q-Analogue of the Jantzen–Schaper Theorem

G James and A Mathas

Department of Mathematics, Imperial College Huxley Building, 180 Queen's Gate, London SW7 2BZ, UK Email: g.james{at}ic.ac.uk and a.mathas{at}ic.ac.uk

Received 5 July 1995. Revision received 16 October 1995.

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 GLn(q) which remain irreducible modulo a prime p not dividing q. 1991 Mathematics Subject Classification: 20C32.

Key Words: Hecke algebras • Schur algebras • Jantzen filtration


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