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

Consider a connected reductive algebraic group $ G $ and a symmetric subgroup$ K $. Let $ \mathfrak{X} = K/B_K \times G/P $ be a double flag variety offinite type, where $ B_K $ is a Borel subgroup of $ K $, and $ P $ a parabolicsubgroup of $ G $. A general argument shows that the orbit space $\mathbb{C}\,\mathfrak{X}/K $ inherits a natural action of the Hecke algebra $\mathscr{H} = \mathscr{H}(K, B_K) $ of double cosets via convolutions. However,to find out the explicit structure of the Hecke module is a quite differentproblem.  In this paper, we determine the explicit action of $ \mathscr{H} $ on $\mathbb{C}\,\mathfrak{X}/K $ in a combinatorial way using graphs for the doubleflag variety of type AIII. As a by-product, we also get the description of therepresentation of the Weyl group on $ \mathbb{C}\,\mathfrak{X}/K $ as a directsum of induced representations.

Action of Hecke algebra on the double flag variety of type AIII