English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $U_q'(\mathfrak{g})$ be a quantum affine algebra with an indeterminate$q$ and let $\mathscr{C}_{\mathfrak{g}}$ be the category of finite-dimensionalintegrable $U_q'(\mathfrak{g})$-modules. We write$\mathscr{C}_{\mathfrak{g}}^0$ for the monoidal subcategory of$\mathscr{C}_{\mathfrak{g}}$ introduced by Hernandez-Leclerc. In this paper, weassociate a simply-laced finite type root system to each quantum affine algebra$U_q'(\mathfrak{g})$ in a natural way, and show that the block decompositionsof $\mathscr{C}_{\mathfrak{g}}$ and $\mathscr{C}_{\mathfrak{g}}^0$ areparameterized by the lattices associated with the root system. We first definea certain abelian group $\mathcal{W}$ (resp. $\mathcal{W}_0$) arising fromsimple modules of $ \mathscr{C}_{\mathfrak{g}}$ (resp.$\mathscr{C}_{\mathfrak{g}}^0$) by using the invariant $\Lambda^\infty$introduced in the previous work by the authors. The groups $\mathcal{W}$ and$\mathcal{W}_0$ have the subsets $\Delta$ and $\Delta_0$ determined by thefundamental representations in $ \mathscr{C}_{\mathfrak{g}}$ and$\mathscr{C}_{\mathfrak{g}}^0$ respectively. We prove that the pair $(\mathbb{R} \otimes_\mathbb{Z} \mathcal{W}_0, \Delta_0)$ is an irreduciblesimply-laced root system of finite type and the pair $( \mathbb{R}\otimes_\mathbb{Z} \mathcal{W}, \Delta) $ is isomorphic to the direct sum ofinfinite copies of $( \mathbb{R} \otimes_\mathbb{Z} \mathcal{W}_0, \Delta_0)$as a root system.

Simply-laced root systems arising from quantum affine algebras