13 problems

Let $V$ be a finite-dimensional irreducible $\boxtimes_q$-module of type $1$, and let $\omega$ be the antiautomorphism of $\boxtimes_q$ from Lemma. Invariant-form conjecture. There…

Let $\Phi$ be a generic tridiagonal-pair parameter array with diameter $d=3$, acting through $A,A^*$ on $V$, and let $w_1,w_2,w_3$ be its weights. Invariant-form conjecture. The fol…

Let $\sigma \\: \Gamma \to 2^V$ be a vertex-induced triangulation of a $(d-1)$-dimensional simplex, and let $k$ be a field. Let $B$ be the symmetric bilinear form on the local face…

Let $G=\operatorname{GL}_{mn}$, let $D$ be the subgroup used in the paper, and let $\sigma,\sigma'\in\operatorname{Irr}G$ be $m$-homogeneous. Consider bilinear forms on…

Let $G=\operatorname{GL}_{mn}$, let $D$ be the subgroup used in the paper, and let $\sigma\in\operatorname{Irr}G$ be $m$-homogeneous. Consider bilinear forms on…

Alternating-form symmetric-operator equality conjecture. There exists a maximal partially complete $b$-singular flag $\mathcal{F}$ of $V$ such that

Let $V$ be the ambient vector space, let $P\subset V\times V$ have density $\delta>0$, and let $c(\delta)$ be the constant in Theorem 1.1, which asserts that there are subspaces…

Let $F$ be the real or complex field, let $\omega$ be a non-degenerate symmetric or skew-symmetric bilinear form on $F^2$, and let $P\subset F^2\setminus\{0\}$ be an $N$-element po…

Bump conjecture. There is a constant $C>0$, independent of $w$ and $\sigma$, such that

Characteristic-two height-two conjecture. There exist a $(d-1)$-fold Pfister form $\pi$ and a $4$-dimensional form $\mathfrak{c}$ of nontrivial determinant such that

Let $R$ be a Frobenius algebra with an ideal $\mathfrak m$ such that … and let $B$ and $B'$ be forms on $R$ related by $B'(r,s)=B(r,su)$ for some $u\in U(R)$. Suppose that $B$ has…

Let $A$ be an $n\times n$ matrix of nonzero entries, and let $x,y$ be chosen independently and uniformly from $\{-1,1\}^n$. For a matrix decomposition $A=A_1+A_2+A_3$, say that…

Non-degeneracy conjecture. (i) If $n=2k+1$, then the bilinear form on the $B_n(\hat{z})$-module $S^{(1)}$ determined by the referenced construction is non-degenerate if and only if…