3 problems

Let $\Gamma=(X,\mathcal R)$ be the bilinear forms graph, let $x,y\in X$ be adjacent vertices, and let $U=U(x,y)$ be the subspace defined earlier. Let $E=E_1$ be the primitive idemp…

Bilinear forms eigenvalue conjecture. For $q\geq 3$, or $q=2$ and $d\neq e$, $B_j(d-j+1)$ is the smallest eigenvalue in the distance-$j$ graph for $1\leq j\leq d$.

Let $B_j(i)$ denote the eigenvalues of the distance-$j$ graph of the bilinear forms association scheme, with parameters $q,d,e$ and $1\le j\le d$. Smallest-eigenvalue conjecture fo…