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Generation of
defect groups and Galois action for $\mathrm{Sp}_4(q)$
Bjorn Cattell-Ravdal, A. A. Schaeffer Fry and Nicole Venner |
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Vol. 19 (2026), No. 3, 423–442
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Abstract |
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The group is a well-known algebraic object and one of the most fundamental structures within mathematics. For a given group, we may correspond the elements to those of a group of invertible matrices, forming a matrix representation of the group. Associated with these representations are characters, obtained by taking the traces of each matrix. Studying these characters, we find that they contain much information about their underlying group. One of the main goals in character theory is to determine what properties about the group can be determined by looking at its characters. We will discuss several recent conjectures on this topic that study properties of certain subgroups known as defect groups. In particular, we prove some such conjectures regarding generation properties of defect -groups for the symplectic group , which is a particular group of matrices over any finite field of odd characteristic. |
Keywords
McKay–Navarro conjecture, Alperin–McKay conjecture,
Alperin–McKay–Navarro conjecture, height-zero characters,
Galois action, defect groups
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Mathematical Subject Classification
Primary: 20C15, 20C33
Secondary: 20C20
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Milestones
Received: 3 August 2024
Accepted: 21 December 2024
Published: 12 June 2026
Communicated by Scott T. Chapman
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Authors |
| Bjorn Cattell-Ravdal | |
| Department of Mathematics and
Statistics Metropolitan State University Denver Denver, CO United States |
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| A. A. Schaeffer Fry | |
| Department of Mathematics University of Denver Denver, CO United States |
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| Nicole Venner | |
| Department of Mathematics and
Statistics Metropolitan State University Denver Denver, CO United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
