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A q ‐Analogue of the Jantzen–Schaper Theorem
Author(s) -
James G,
Mathas A
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000099
Subject(s) - mathematics , modulo , mathematics subject classification , prime (order theory) , pure mathematics , type (biology) , schur algebra , field (mathematics) , irreducible representation , algebra over a field , discrete mathematics , combinatorics , classical orthogonal polynomials , ecology , gegenbauer polynomials , orthogonal polynomials , biology
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 . 1991 Mathematics Subject Classification : 20C32.