Chern Medal Lecture: Crystal bases and categorifications — Masaki Kashiwara — ICM2018

Crystal bases and categorifications Masaki Kashiwara Abstract: A crystal basis is a basis at q=0 of the half U−q (g) of a quantum group U q (g) . It lifts to a true basis in two ways: a lower global basis and an upper global basis. At q=1 , the upper global basis becomes a basis of the coordinate ring C[n] of the nilpotent part n. As we can imagine from the fact that C[n] is a commutative ring, the upper global basis has good multiplicative properties, which is indeed one of the motivations of the introduction of the notion of cluster algebras by Fomin–Zelevinsky. In this talk, we discuss such multiplicative properties using its categorification by quiver Hecke algebras introduced by Rouquier and Khovanovi–Lauda. This is partly a joint work with Seok-Jin Kang, Myungho Kim and Se-jin Oh. Unfortunately, the abstract in description has text only limitation. To see correct abstract look at icm2018.org ICM 2018 - International Congress of Mathematicians © www.icm2018.org     Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.