5 problems

Let $\mathbb{K}$ be a field, let $q\in\mathbb{K}^*$ be not a root of unity, and let ${\mathcal O}_q(M_n)$ be the quantisation of the ring of regular functions on $n\times n$ matric…

Let $B^*$ be the dual canonical basis of the quantum matrix algebra $O_q(M(n))$. Call $b\in B^*$ decomposable if there exist $m\in\mathbb Z$ and $b_1,b_2\in B^*$ such that…

Primitive-proportion conjecture. As $n\rightarrow\infty$, the proportion of $\mathcal{H}$-primes that are primitive tends to

Exponential enumeration conjecture. For every positive integer $n$,

Primitive-prime enumeration conjecture. The number of primitive $\mathcal{H}$-primes in ${\mathcal O}_q(M_{3,n})$ is