The next CART seminar is scheduled for Apr 3rd (Fri), 10:30 - 11:30 (Korea time).

Speaker: Heizo Sakamoto (The University of Tokyo)

Title: Classification of real and imaginary modules of quantum affine algebras in monoidal categorifications of affine cluster algebras

Abstract: A finite-dimensional module $L$ over an affine quantum group is called real if the tensor product $L \otimes L$ is irreducible. It is known that for an appropriately chosen subcategory $\mathcal{C}$ of the category of finite-dimensional representations, the Grothendieck ring $K(\mathcal{C})$ has a cluster algebra structure in which cluster monomials correspond to irreducible modules (categorification of cluster algebras).In such a category $\mathcal{C}$, Hernandez-Leclerc conjectured that an irreducible module corresponds to a cluster monomial if and only if it is a real module. This conjecture remains generally open, except for cases where the categorified cluster algebra is of finite type. In this talk, I will construct subcategories that categorify cluster algebras of affine type and explain that the conjecture holds within these categories. 

You can join the seminar via the following

Zoom link:  https://kias-re-kr.zoom.us/j/86178377083?pwd=znH3EbxqjXmDCiVnv4OTl3SgJHlxva.1

Meeting ID: 861 7837 7083

Password: 172764

Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/).

Looking forward to seeing you at the seminar!

Best regards,

Sin-Myung Lee