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

For any simple complex Lie algebra $\mathfrak{g}$, we show that the degreesof the "ADO" link polynomials coming from the unrolled restricted quantum group$\overline{U}^H_q(\mathfrak{g})$ at a root of unity give lower bounds to theSeifert genus of the link. We give a direct simple proof of this fact relyingon a Seifert surface formula involving universal$\mathfrak{u}_q(\mathfrak{g})$-invariants, where $\mathfrak{u}_q(\mathfrak{g})$is the small quantum group. We give a second proof by showing that theinvariant $P_{\mathfrak{u}_q(\mathfrak{b})}^{\theta}(K)$ of our previous workcoincides with such ADO invariants, where $\mathfrak{u}_q(\mathfrak{b})$ is theBorel part of $\mathfrak{u}_q(\mathfrak{g})$. To prove this, we show thatequivariantizations of relative Drinfeld centers of crossed productsessentially contain unrolled restricted quantum groups, a fact that could be ofindependent interest.

Genus bounds from unrolled quantum groups at roots of unity