Hermitian forms graph absolute eigenvalue conjecture

Let Qq(d)Q_q(d) be the Hermitian forms scheme on the d×dd\times d Hermitian matrices over Fq2\mathbb{F}_{q^2}, and let Qj(i)Q_j(i) denote the eigenvalue indexed by ii in its distance-jj graph.

Hermitian absolute eigenvalue conjecture. Let d3d\geq 3. Then

Qj(i)<Qj(1)|Q_j(i)| < |Q_j(1)|

for 2id2\leq i\leq d.

The theorem in the paper proves this assertion under the stated Hermitian-forms hypotheses, so it is resolved there.

Sources & referencesView supporting material

Primary source

Sebastian M. Cioabă and Himanshu Gupta, “On the eigenvalues of Grassmann graphs, Bilinear forms graphs and Hermitian forms graphs”, arXiv:2102.10155 (2021).

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