2 problems

Assume that no $i\in I$ satisfies $\theta(i)=i$, and use the lattice $L_\theta$, its bar-conjugate $L_\theta^-$, and the integral module $(V_\theta)_\mathbf A$ defined from the bar…

Let $L_\theta(\lambda)$ be the crystal lattice, let $c(L_\theta(\lambda))$ denote its bar-conjugate lattice, and let $V_\theta(\lambda)^{\mathrm{up}}_{\mathbf A}$ be the dual latti…