表現論セミナー Generalization of quantum Grothendieck rings（OH Se-jin氏）

Grothendieck rings $C_g$ of finite dimensional modules over quantum affine algebras have been intensively studied since they are related to various branches of mathematics and mathematical physics. The quantization of $C_g$ introduced by Nakajima and Varanolo-Vasserot, called quantum Grothendieck ring, provides a Kazhdan-Lusztig algorithm for Jordan-Holder multiplicity of simple modules in standard modules for ADE cases. In this talk, I would like to introduce the generalization of the quantum Grothendieck ring and recent progress about it. If time permits, I would like to discuss the quantum positivity of KR-polynomials. This talk is based on the results with my collaborators, Fujita, Jang, Hernandez, Lee, Kashiwara, Kim, Park and Oya.