- Date : 2022-10-11 (Tue) 10:00 ~ 11:30
2022-10-12 (Wed) 13:00 ~ 14:30
Place : Zoom
- Speaker : 오세진 (이화여자대학교)
- Title : (q,t)-Cartan matrix and representation theories related to the specializations of the matrix
- Abstract :
In the last of 1990's, Frenkel and Reshetikhin introduced the two-parameter deform of Cartan matrix of finite type, usually called (q,t)-Cartan matrix, to construct two-parameter deformed version of W-algebra with a motivation arising from mathematical physics. Interestingly enough, it is proved that the q-deformed W-algebra W_q is isomorphic to the Grothedieck ring of quantum affine algebra, when it is of simply-laced finite type. In this talk, we will first see the relationship between $t=1$-specialization of (q,t)-Cartan matrix and the representation theory of quantum affine algebra by using finite root system and Dynkin quivers. If time permits, I would like to explain the relationship between $q=1$-specialization of (q,t)-Cartan matrix and the representation theory of quiver Hecke algebra, based on my works with collaborators. During the talk, I will mainly use easy examples such as type $A_3$ or $C_3$.