Title: Foldings of quantum groups and of KLR algebras

Abstract: Let U be the quantum group associated to a Cartan datum X, with vertex set I. A diagram automorphism s on I induces a Cartan datum X', where the vertex set I' is the set of s-orbits in I. Let U' be the quantum group associated to X'. The folding theory of quantum groups discusses the relationship between (U, s) and U'.  In this talk, we explain that there exists two types of folding theory of quantum groups, one is established by Lusztig, and another by Ma-Shoji-Zhou. KLR algebra is an algebra introduced by Khovanov-Lauda and Rouquier, independently. KLR algebras give a categorification of quantum groups. McNamara established a folding theory for KLR algebras, motivated by Lusztig's theory for quantum groups. In this talk, we give a positive answer to the question posed by McNamara, by making use of two types folding theory for quantum groups mentioned above.