The orthogonal character table of SL2(q)
Oliver Braun, Gabriele Nebe
TL;DR
This paper investigates the orthogonal character table of SL2(q), focusing on rational invariants of invariant quadratic forms on real irreducible representations, and addresses an open question for even square q.
Contribution
It determines the rational invariants of SL2(q)-invariant quadratic forms and explores unresolved cases for even square q.
Findings
Rational invariants of invariant quadratic forms are characterized.
Open question remains for even square q cases.
Provides a comprehensive analysis of the orthogonal character table.
Abstract
The rational invariants of the SL_2(q)-invariant quadratic forms on the real irreducible representations are determined. There is still one open question (see Remark 6.5) if q is an even square.
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