Some Simple Projective Brauer Quotients of Simple Modules for the Symmetric Groups in Characteristic Two

AbstractThe symmetric group on a set acts transitively on the set of its subsets of a fixed size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from simplicial homology. The main results determine when these chain complexes are exact and when they are split exact. As a corollary we obtain a new explicit construction of the basic spin modules for the symmetric group.

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The complexities of some simple modules of the symmetric groups

Bulletin of the London Mathematical Society ◽

10.1112/blms/bds118 ◽

2012 ◽

Vol 45 (3) ◽

pp. 497-510 ◽

Cited By ~ 2

Author(s):

Kay Jin Lim ◽

Kai Meng Tan

Keyword(s):

Symmetric Groups ◽

Simple Modules

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Vertices of Low-Dimensional Simple Modules for Symmetric Groups

Communications in Algebra ◽

10.1080/00927870802182606 ◽

2008 ◽

Vol 36 (12) ◽

pp. 4521-4539 ◽

Cited By ~ 3

Author(s):

Susanne Danz

Keyword(s):

Symmetric Groups ◽

Simple Modules ◽

Low Dimensional

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On the Vertices of Simple Modules for Symmetric Groups

Communications in Algebra ◽

10.1080/00927870802174223 ◽

2008 ◽

Vol 36 (11) ◽

pp. 3980-3998

Author(s):

Bosco Fotsing

Keyword(s):

Symmetric Groups ◽

Simple Modules

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The Vertices of a Class of Specht Modules and Simple Modules for Symmetric Groups in Characteristic 2

Algebra Colloquium ◽

10.1142/s100538671200082x ◽

2012 ◽

Vol 19 (spec01) ◽

pp. 987-1016 ◽

Cited By ~ 1

Author(s):

Susanne Danz ◽

Karin Erdmann

Keyword(s):

Symmetric Groups ◽

Specht Modules ◽

Simple Modules ◽

Characteristic 2

We study Specht modules S(n-2,2) and simple modules D(n-2,2) for symmetric groups 𝔖n of degree n over a field of characteristic 2. In particular, we determine the vertices of these modules, and also provide some information on their sources.

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