The Jantzen sum formula for cyclotomic 𝑞–Schur algebras

James, Gordon; Mathas, Andrew

doi:10.1090/S0002-9947-00-02492-2

The Jantzen sum formula for cyclotomic $q$–Schur algebras
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by Gordon James and Andrew Mathas PDF

Trans. Amer. Math. Soc. 352 (2000), 5381-5404 Request permission

Abstract:

The cyclotomic $q$-Schur algebra was introduced by Dipper, James and Mathas, in order to provide a new tool for studying the Ariki-Koike algebra. We here prove an analogue of Jantzen’s sum formula for the cyclotomic $q$-Schur algebra. Among the applications is a criterion for certain Specht modules of the Ariki-Koike algebras to be irreducible.

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