A new proof of Nakayama's Conjecture via Brauer quotients of Young modules
William O'Donovan
TL;DR
This paper offers a new inductive proof of Nakayama's Conjecture on symmetric group blocks by establishing key properties of Brauer quotients of Young modules.
Contribution
It introduces a self-contained proof of Brauer quotients of Young modules and applies these results to prove Nakayama's Conjecture.
Findings
Established main properties of Brauer quotients of Young modules
Provided a new inductive proof of Nakayama's Conjecture
Enhanced understanding of symmetric group block structure
Abstract
We provide a self-contained proof of the main properties of Brauer quotients of Young modules. We then use these results to give a new inductive proof of Nakayama's Conjecture on the blocks of the symmetric group.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology