Categorified Crystal Bases on Localized Quantum Coordinate Rings

Explore advanced concepts in quantum algebra and representation theory through this 45-minute lecture by Toshiki Nakashima from Sophia University, Tokyo. Delve into the categorification of crystal bases on localized quantum coordinate rings, examining the relationship between quiver Hecke algebras and quantum coordinate rings. Learn about the localization of monoidal categories, the construction of crystal structures on self-dual simple objects, and the isomorphism between these structures and cellular crystals. Gain insights into the localized version of the categorification of the crystal base B(∞) for the subalgebra U^−_q(g) of the quantum algebra U_q(g), building upon the work of Lauda-Vazirani.