Morit7a equivalences of cyclotomic Hecke algebras of type G(r, p, n)

Jun Hu*, Andrew Mathas

*Corresponding author for this work

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Abstract

We prove a Morita reduction theorem for the cyclotomic Hecke algebras ℋr, p, n(q, Q) of type G(r, p, n) with p > 1 and n ≧ 3. As a consequence, we show that computing the decomposition numbers of ℋr, p, n(Q) reduces to computing the p′-splittable decomposition numbers (see Definition 1.1) of the cyclotomic Hecke algebras ℋr′, p′, n′(Q′), where 1 ≦ r′ ≦ r, 1 ≦ n′ ≦ n, p′ | p and where the parameters Q′ are contained in a single (ε′, q)-orbit and ε′ is a primitive p′th root of unity.

Original languageEnglish
Pages (from-to)169-194
Number of pages26
JournalJournal fur die Reine und Angewandte Mathematik
Issue number628
DOIs
Publication statusPublished - Mar 2009

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Hu, J., & Mathas, A. (2009). Morit7a equivalences of cyclotomic Hecke algebras of type G(r, p, n). Journal fur die Reine und Angewandte Mathematik, (628), 169-194. https://doi.org/10.1515/CRELLE.2009.022