Ewha Womans University Mathematics

Research Areas

Prof. Se-jin Oh

Representation Theory Lab

Faculty Introduction
Prof. Se-jin Oh
Prof. Se-jin Oh
Research Area
  • Categorifical representation theory
  • Combinatorial representation theory
Lab Introduction
Combinatorial Representation Theory

We study variety algebraic objects by reflecting them into vector spaces. In particular, we use Young-object and Auslander-Retien quiver, which is very well-known combinaorial object, to define algebraic actions and study the phenomena happening by the actions to study those algebraic objects. We focus on quantum affine algebras and quiver Hecke algebra as the algebraic objects, which have origins from mathematical physics, by using the combinatorial tools.

Categorical Representation Theory

We study the ring spanned by representations over variety algebraic objects, whose multiplication is a tensor indeed. This kind of study is established by Grothendieck, the french mathematian, around 1970's. In particular, we are interested in the relation between categorical representation theory and cluster algebra theory, both of them have natural positivity phenomena.

Major research projects and Research achievements
Major research projects and Research achievements
  • Proofs on the categorical positivity for the Grothendieck ring over quantum affine algebras
  • Proofs on the monoidal categorifications of modules over quiver Hecke algebras.
  • Establishing the criterion for the monoidal super-categorification.
  • Find closed formulae for dimensions of the weight spaces of representation over quantum affine algebras.
Selected research papers
  • Masaki Kashiwara, Myungho Kim, Se-jin Oh* and Euiyong Park, Monoidal categorification and quantum affine algebras, Compositio Mathematica. Volume 156, Issue 5 May 2020 , pp. 1039-1077.
  • Young-Hun Kim, Se-jin Oh and Young-Tak Oh, Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras, Advances in Mathematics Volume 374, 18 November 2020, 107336.
  • Jang Soo Kim, Kyu-Hwan Lee and Se-jin Oh*, Weight multiplicities and Young tableaux through affine crystals, to be appeared in Memoirs of the American Mathematical Society arXiv:1703.10321.
  • Masaki Kashiwara and Se-jin Oh*, Categorical relations between Langlands dual quantum affine algebras: Doubly laced types, Journal of Algebraic Combinatorics (2019) 49(4) 401-435.
  • Seok-Jin Kang, Masaki Kashiwara, Myungho Kim and Se-jin Oh, Monoidal categorification of cluster algebra, Journal of American Mathematical Society, 31 (2018), 349-426(13).