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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $\mathfrak g$ be a complex semisimple Lie algebra. We obtain newproperties of the $q$-analogue of weight multiplicities in finite-dimensionalrepresentations of $\mathfrak g$. In particular, it is proved that certainweighted sum of $q$-analogues of all weights of a representation $V$ equals the$q$-analogue of the zero weight multiplicity in the reducible representation$V\otimes V^*$. This also provides another formula for the $\mathbbZ[q]$-valued symmetric bilinear form on the character ring of $\mathfrak g$that was introduced by R.Gupta (Brylinski) in 1987.

On Lusztig's $q$-analogues of all weight multiplicities of a representation