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The decomposition numbers of Hecke algebras of type \(F_ 4\) with unequal parameters. (English) Zbl 0830.20062

Summary: The purpose of this paper is to calculate the decomposition numbers for Hecke algebras of type \(F_4\) (and \(C_3\)) with unequal parameters. The problem is reduced to specifying decomposition maps of the generic Hecke algebras. The concept of Kazhdan-Lusztig polynomials and left cells serves to determine their irreducible representations. We also prove a result about the minimal ring over which the irreducible representations of the generic algebras can be realized.

MSC:

20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
20C33 Representations of finite groups of Lie type

Software:

GAP; Maple
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References:

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