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

By a theorem of D. Wigner, an irreducible unitary representation withnon-zero $(\frak{g},K)$-cohomology has trivial infinitesimal character, andhence up to unitary equivalence, these are finite in number. We have determinedthe number of equivalence classes of these representations and the Poincar\'{e}polynomial of cohomologies of these representations for the Lie group$SO_0(2,m)$ for any positive integer $m.$ We have also determined, among these,which are discrete series representations and holomorphic discrete seriesrepresentations.

Irreducible unitary representations with non-zero relative Lie algebra cohomology of the Lie group $SO_0(2,m)$