Groups are mathematical objects used to describe the structure of symmetries, with
one of the most canonical examples being the set of invertible matrices of a given size
over a fixed base field. For a given group, a matrix representation leverages this by
providing a way to represent each of its elements as an invertible matrix. The
information about the (complex) representations of a finite group can be condensed by
instead considering the trace of the matrices, yielding a function known as a character.
One of the overarching themes in character theory is to determine what properties
about a finite group or its subgroups can be obtained by studying its characters. We
study a conjecture that proposes a correlation between the makeup of a group’s
irreducible characters and the properties of certain subgroups known as defect
groups. In particular, we prove the conjecture for the finite symplectic groups
.
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