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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove a case of a positivity conjecture of Mihalcea-Singh, concerned withthe local Euler obstructions associated to the Schubert stratification of theLagrangian Grassmannian LG(n,2n). Combined with work ofAluffi-Mihalcea-Sch\"urmann-Su, this further implies the positivity of theMather classes for Schubert varieties in LG(n,2n), which Mihalcea-Singh hadverified for the other cominuscule spaces of classical Lie type. Building onthe work of Boe and Fu, we give a positive recursion for the local Eulerobstructions, and use it to show that they provide a positive count ofadmissible labelings of certain trees, analogous to the ones describingKazhdan-Lusztig polynomials. Unlike in the case of the Grassmannians in types Aand D, for LG(n,2n) the Euler obstructions e_{y,w} may vanish for certain pairs(y,w) with y <= w in the Bruhat order. Our combinatorial description allows usto classify all the pairs (y,w) for which e_{y,w}=0. Restricting to the bigopposite cell in LG(n,2n), which is naturally identified with the space of n xn symmetric matrices, we recover the formulas for the local Euler obstructionsassociated with the matrix rank stratification.

Euler obstructions for the Lagrangian Grassmannian