The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups

J. M. Lataille; Peter Sin; Pham Huu Tiep

doi:10.1016/S0021-8693(03)00229-1

The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups

J. M. Lataille, Peter Sin, Pham Huu Tiep

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

This paper studies the permutation representation of the symplectic group Sp(2m, F_q), where q is odd, on the 1-spaces of its natural module. The complete submodule lattice for the modulo ℓ reduction of this permutation module is known for all odd primes ℓ not dividing q. In this paper we determine the complete submodule lattice for the mod 2 reduction. Similar results are then obtained for the orthogonal group O(5, F_q).

Original language	English (US)
Pages (from-to)	463-483
Number of pages	21
Journal	Journal of Algebra
Volume	268
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(03)00229-1
State	Published - Oct 15 2003
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0021-8693(03)00229-1

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title = "The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups",

abstract = "This paper studies the permutation representation of the symplectic group Sp(2m, Fq), where q is odd, on the 1-spaces of its natural module. The complete submodule lattice for the modulo ℓ reduction of this permutation module is known for all odd primes ℓ not dividing q. In this paper we determine the complete submodule lattice for the mod 2 reduction. Similar results are then obtained for the orthogonal group O(5, Fq).",

author = "Lataille, {J. M.} and Peter Sin and Tiep, {Pham Huu}",

note = "Funding Information: * Corresponding author. E-mail addresses: jlataill@valdosta.edu (J.M. Lataille), sin@math.ufl.edu (P. Sin), tiep@math.ufl.edu (P.H. Tiep). 1 The author was supported by NSF grant number DMS 0071060. 2 The author was supported by NSF grant number DMS 0070647.",

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T1 - The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups

AU - Lataille, J. M.

AU - Sin, Peter

AU - Tiep, Pham Huu

N1 - Funding Information: * Corresponding author. E-mail addresses: jlataill@valdosta.edu (J.M. Lataille), sin@math.ufl.edu (P. Sin), tiep@math.ufl.edu (P.H. Tiep). 1 The author was supported by NSF grant number DMS 0071060. 2 The author was supported by NSF grant number DMS 0070647.

PY - 2003/10/15

Y1 - 2003/10/15

N2 - This paper studies the permutation representation of the symplectic group Sp(2m, Fq), where q is odd, on the 1-spaces of its natural module. The complete submodule lattice for the modulo ℓ reduction of this permutation module is known for all odd primes ℓ not dividing q. In this paper we determine the complete submodule lattice for the mod 2 reduction. Similar results are then obtained for the orthogonal group O(5, Fq).

AB - This paper studies the permutation representation of the symplectic group Sp(2m, Fq), where q is odd, on the 1-spaces of its natural module. The complete submodule lattice for the modulo ℓ reduction of this permutation module is known for all odd primes ℓ not dividing q. In this paper we determine the complete submodule lattice for the mod 2 reduction. Similar results are then obtained for the orthogonal group O(5, Fq).

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DO - 10.1016/S0021-8693(03)00229-1

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AN - SCOPUS:0242425105

SN - 0021-8693

VL - 268

SP - 463

EP - 483

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups

Abstract

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