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

In this paper we develop machinery for studying sequences of representationsof any of the three families of classical Weyl groups, extending work ofChurch, Ellenberg, Farb, and Nagpal on the symmetric groups S_n to the signedpermutation groups B_n and the even-signed permutation groups D_n. For eachfamily W_n, we present an algebraic framework where a sequence V_n ofW_n-representations is encoded into a single object we call an FI_W-module. Weprove that if an FI_W-module V satisfies a simple finite generation conditionthen the structure of the sequence is highly constrained. One consequence isthat the sequence is uniformly representation stable in the sense ofChurch-Farb, that is, the pattern of irreducible representations in thedecomposition of each V_n eventually stabilizes in a precise sense. Using thetheory developed here we obtain new results about the cohomology of generalizedflag varieties associated to the classical Weyl groups, and more generally ther-diagonal coinvariant algebras.  We analyze the algebraic structure of the category of FI_W-modules, andintroduce restriction and induction operations that enable us to studyinteractions between the three families of groups. We use this theory to proveanalogues of Murnaghan's 1938 stability theorem for Kronecker coefficients forthe families B_n and D_n. The theory of FI_W-modules gives a conceptualframework for stability results such as these.

FI_W-modules and stability criteria for representations of the classical Weyl groups