Irreducible tensor products for symmetric groups in characteristic 2

Lucia Morotti

doi:10.1112/plms.12127

Irreducible tensor products for symmetric groups in characteristic 2

Proceedings of the London Mathematical Society ◽

10.1112/plms.12127 ◽

2018 ◽

Vol 116 (6) ◽

pp. 1553-1598 ◽

Cited By ~ 4

Author(s):

Lucia Morotti

Keyword(s):

Symmetric Groups ◽

Tensor Products ◽

Irreducible Tensor ◽

Characteristic 2

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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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Cohomological Invariants in Positive Characteristic

International Mathematics Research Notices ◽

10.1093/imrn/rnaa321 ◽

2021 ◽

Author(s):

Burt Totaro

Keyword(s):

Positive Characteristic ◽

Differential Forms ◽

Symmetric Groups ◽

Characteristic P ◽

Motivic Cohomology ◽

Cohomological Invariants ◽

Group Schemes ◽

Characteristic 2 ◽

Theory Of Fields ◽

Mod P

Abstract We determine the mod $p$ cohomological invariants for several affine group schemes $G$ in characteristic $p$. These are invariants of $G$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology based on differential forms. In particular, we find the mod 2 cohomological invariants for the symmetric groups and the orthogonal groups in characteristic 2, which Serre computed in characteristic not 2. We also determine all operations on the mod $p$ étale motivic cohomology of fields, extending Vial’s computation of the operations on the mod $p$ Milnor K-theory of fields.

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Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498815500309 ◽

2014 ◽

Vol 14 (03) ◽

pp. 1550030 ◽

Cited By ~ 3

Author(s):

Adam Chapman

Keyword(s):

Quadratic Forms ◽

Symplectic Group ◽

Tensor Products ◽

Base Field ◽

Quaternion Algebras ◽

Characteristic 2

We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain equivalences for quadratic forms, both in characteristic 2 and not 2, we provide chain equivalences for tensor products of quaternion algebras over fields with no nontrivial 3-fold Pfister forms. The chain equivalence for biquaternion algebras in characteristic 2 is also obtained in this process, without any assumption on the base-field.

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