3 problems

Let $Q(x)=x^3-\alpha x^2-\beta x-1$, and let $H(Q,n)=\mathbb{C}[B_n]/(Q(b_j);\,j=1,\dots,n-1)$ be the cubic Hecke algebra. The invariant $I_{(\alpha,\beta)}$ is defined by a Markov…

Let $t_3^0$ be the Markov trace on the specialized algebra described by the conditions $t_3^0(1)=t_3^0(s_1)=0$ and $t_3^0(s_1s_2)=1$. Markov-trace extension conjecture. The trace…

For $n\geq 3$, let $\mathcal{B}_n^{\pm}$ be the specialized algebra, let $\mathcal{I}_n^{\pm}$ be its defining ideal, and let…