 Date : 20221011 (Tue) 10:00 ~ 11:30
20221012 (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 twoparameter deform of Cartan matrix of finite type, usually called (q,t)Cartan matrix, to construct twoparameter deformed version of Walgebra with a motivation arising from mathematical physics. Interestingly enough, it is proved that the qdeformed Walgebra W_q is isomorphic to the Grothedieck ring of quantum affine algebra, when it is of simplylaced 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 $C_3$.