10 problems

Brauer specialization conjecture. There is a subalgebra $B^{(0)}$ of $B$ defined over $E$, containing a spanning set of $B$, such that after reduction modulo $(l-1)$ one obtains a…

Type D BMW dimension conjecture. The dimension of $B({\rm D}_n)$ is

Coclique ideal conjecture. If $J$ is a coclique of $M$ of size $i>1$, then $I_J$ is an ideal properly contained in $I_{i-1}$.

BMW deformation conjecture. A similar deformation exists for the spherical simply laced types, with the pictures forming the monomial basis of the Brauer algebra indexed by a combi…

Center conjecture. The center of $B_n(q,q^{2a})$ is

Let $\operatorname{BMW}^{\mathfrak{Leg}}_n$ be the Legendrian BMW algebra and let $\operatorname{BMW}^{\infty}_n$ be the specialized BMW algebra, with…

Let $d$ and $n$ be positive integers, and let $F_{d,n}$ denote the framization of the Birman–Wenzl–Murakami algebra constructed in the paper. A Markov trace conjecture asserts that…

Let $G_1,\ldots,G_{n-1}$ be the matrices describing the actions of the BMW generators $g_1,\ldots,g_{n-1}$ on the spanning elements of a vector space $W$, and define … Here…

Let $T$ denote the left action on the Lawrence–Krammer space of the sum of all conjugates of the BMW generators $e_i$ by products of the generators $g_i$. Fix $r\in\mathbb{C}$, and…

Let $n$ be an integer with $n\geq 3$. Let $\mathcal{H}_{F,r^2}(n)$ be the BMW algebra of type $A_{n-1}$ over $F$, and let $\mathcal{V}^{(n)}$ be the Lawrence–Krammer space. Assume…