8 problems

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

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…

Let $(\Psi,\mu,w)$ be a labeled root ideal with partition $\mu$, let $j\geq0$, and let $X_w$ be the corresponding Schubert variety. Write $\mathfrak u_\Psi$ for the root subspace a…

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…

Let $B$ and $B'$ be tensor products of Kirillov–Reshetikhin crystals satisfying the hypotheses of Theorems demazure decomposition and red in the source, and let $D_\ell(B)$ and…

Let $U_q(\mathfrak{g})$ be a quantum affine algebra, and let $\kappa$ denote the mixing index arising in the tensor product-like path realization of its Demazure crystals. Mixing-i…

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…