Nilpotency indices for quantum Schubert cell algebras

Garrett Johnson, Hayk Melikyan

We study quantum analogs of $\mathrm{ad}$-nilpotency and Engel identities in quantum Schubert cell algebras ${\mathcal{U}}_q^{+}[w]$. For each pair of Lusztig root vectors, $X_μ…