Resumen de Canonical bases of quantum Schubert cells and their symmetries

Arkady Berenstein, Jacob Greenstein

• The goal of this work is to provide an elementary construction of the canonical basis B(w) in each quantum Schubert cell Uq (w) and to establish its invariance under modified Lusztig’s symmetries. To that effect, we obtain a direct characterization of the upper global basis Bup in terms of a suitable bilinear form and show that B(w) is contained in Bup and its large part is preserved by modified Lusztig’s symmetries.