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Publication# Generalized Blocks of Unipotent Characters in the Finite General Linear Group

Journal paper

Abstract

In an article of 2003, Kulshammer, Olsson, and Robinson defined l-blocks for the symmetric groups, where l is an arbitrary integer, and proved that they satisfy an analogue of the Nakayama Conjecture. Inspired by this work and the definitions of generalized blocks and sections given by the authors, we give in this article a definition of d-sections in the finite general linear group, and construct d-blocks of unipotent characters, where d is an arbitrary integer. We prove that they satisfy one direction of an analogue of the Nakayama Conjecture, and, in some cases, prove the other direction. We also prove that they satisfy an analogue of Brauer's Second Main Theorem.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

General linear group

In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a gr

Arbitrary-precision arithmetic

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