5 problems

Let $V_\theta(\lambda)$ be the symmetric-crystal module above, let $L_\theta(\lambda)$ be its crystal lattice, let $\overline{L_\theta(\lambda)}$ be its bar-invariant counterpart,…

Let $I$ be the index set of a symmetrizable Cartan datum, let $\theta$ be an involutive Dynkin-diagram automorphism with no fixed point, and let $V_\theta(\lambda)$ be the irreduci…

Let $V_\theta(\lambda)$ be the symmetric-crystal module associated with a Dynkin diagram involution $\theta$ and a dominant integral weight $\lambda$ fixed by $\theta$, and let its…

The paper concerns affine Hecke algebras of type $B$, symmetric crystals, and the module $V_\theta(\lambda)$, whose lower global basis is associated with the symmetric-crystal stru…

Symmetric-crystal parametrization conjecture. The finite-dimensional irreducible $\mathcal{H}^B$-modules of type $J$ have representatives $\{L_b\mid b\in B_\theta(0)\}$ satisfying