Constructible characters and canonical bases

We give closed formulas for all vectors of the canonical basis of a level 2 irreducible integrable representation of $U_v(sl_\infty)$. These formulas coincide at v=1 with Lusztig's formulas for the constructible characters of the Iwahori-Hecke algebras of type B and D.Comment: 16 page

Row and column removal in the q-deformed Fock space

Analogues of James's row and column removal theorems are proved for the q-decomposition numbers arising from the canonical basis in the q-deformed Fock space