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Decomposition matrices for d-Harish-Chandra series: the exceptional rank two cases

Part of: Linear algebraic groups and related topics Representation theory of groups

Published online by Cambridge University Press:  01 November 2011

Maria Chlouveraki  and
Hyohe Miyachi
Maria Chlouveraki
Affiliation:
School of Mathematics, University of Edinburgh, JCMB, Room 5610 King’s Buildings Edinburgh EH9 3JZ, United Kingdom (email: maria.chlouveraki@ed.ac.uk)
Hyohe Miyachi
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya Aichi, 464-8602, Japan (email: miyachi@math.nagoya-u.ac.jp)

Abstract

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We calculate all decomposition matrices of the cyclotomic Hecke algebras of the rank two exceptional complex reflection groups in characteristic zero. We prove the existence of canonical basic sets in the sense of Geck–Rouquier and show that all modular irreducible representations can be lifted to the ordinary ones.

MSC classification

Secondary: 20C08: Hecke algebras and their representations 20G40: Linear algebraic groups over finite fields 20C20: Modular representations and characters
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 271 - 290
Copyright
Copyright © London Mathematical Society 2011

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