5 problems

A Demazure crystal is denoted by $\mathcal{B}_{w,\lambda}$, where the crystal is of type $A$, normal, and finite. A flagged skew tableau crystal is the crystal of flagged skew tabl…

Symplectic Demazure crystal conjecture. The crystal $\mathrm{BRF}^{\mathsf{Sp}}_n(z,\phi)$ is a direct sum of Demazure $\mathfrak q_n$-crystals.

Fix $a\in I_0$, set $c=\min\{c_b\mid A_{ba}\neq 0\}$, and let $\ell\geq\lceil m/c\rceil$. Write $L(k)=\left\lfloor\frac{mA_{ba}-k}{A_{ab}}\right\rfloor$. Q-system Demazure decompos…

Demazure-crystal expansion conjecture. There exists a reduced expression of the longest Weyl-group element $\mathbf i=(i_1,\ldots,i_N)$ and a sign $p=(p_{i,j})_{i\ne j}$ such that,…

Let $I$ be the index set of the root system, let $\mathbf i=(i_1,\ldots,i_N)$ be a reduced expression of the longest Weyl-group element, and let $p=(p_{i,j})_{i\ne j}$ be the assoc…