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

The irreducible representations $\phi_n^1$ and $\phi_n^2$ of the symplecticgroup $G_n=Sp_{2n}(P)$ over an algebraically closednfield $P$ of characteristic$p>2$ with highest weights $\omega_{n-1}+\frac{p-3}{2}\omega_n$ and$\frac{p-1}{2}\omega_n$, respectively, are investigated. It is proved that thedimension of $\phi_n^i$ ($i=1,2$) is equal to $(p^n+(-1)^i )/2$, all weightmultiplicities of these representations are equal to $1$, their restrictions tothe group $G_k$ naturally embedded into $G_n$ are completely reducible withirreducible constituents $\phi_k^1$ and $\phi_k^2$, and their restrictions to$Sp_{2n}(p)$ can be obtained as the result of the reduction modulo $p$ ofcertain complex irreducible representations of the group $Sp_{2n}(p)$.

Representations of dimensions $(p^n\pm 1)/2$ of the symplectic group of degree $2n$ over a field of characteristic $p$