4 problems

Q-invariant and barred P-invariant generation conjecture. The field ${\rm Inv}_{R\overline{R}}$ is generated by the $Q$-invariants, barred $P$-invariants, and shape invariants. Eve…

Q-invariant and shape-invariant generation conjecture. The field ${\rm Inv}_{R\overline{e}}$ is generated by the $Q$-invariants and shape invariants. Moreover, every element of…

Loop symmetric functions are polynomial invariants of the birational symmetric-group action induced by the one-row geometric $R$-matrix, and their tropicalizations can be considere…

Let $B=B^{1,s_1}\otimes\cdots\otimes B^{1,s_m}$ be a product of one-row crystals, let $p=b_1\otimes\cdots\otimes b_m\in B$, and define $x_j^{(i+j-1)}$ to be the number of occurrenc…