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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G$ be a simple algebraic group over an algebraically closed field $K$and let $N = N_G(T)$ be the normalizer of a fixed maximal torus $T\leq G$.Further, let $U$ be the unipotent radical of a fixed Borel subgroup $B$ thatcontains $T$ and let $U^-$ be the unipotent radical of the opposite Borelsubgroup $B^-$. The Bruhat decomposition implies the decomposition $G =NU^-UN$. The Zariski closed subset $U^-U\subset G$ is isomorphic to the affinespace $A_K^m$ where $m = \dim G -\dim T$ is the number of roots in thecorresponding root system. Here we construct a subgroup $\mathcal{N}\leq\operatorname{Cr}_m(K)$ that ``acts partially'' on $A_K^m\approx\mathcal{U}$and we show that there is one-to-one correspondence between the orbits of sucha partial action and the set of double cosets $\{NgN\}$. Here we also calculatethe set $\{g_\alpha\}_{\alpha \in \mathfrak A}\subset \mathcal{U}$ in thesimplest case $G = \operatorname{SL}_2(\mathbb{C})$.

Double cosets $NgN$ of normalizers of maximal tori of simple algebraic groups and orbits of partial actions of Cremona subgroups