Spanning Configurations and Representation Stability

Brendan Pawlowski, Eric Ramos, Brendon Rhoades

Research output: Contribution to journalArticlepeer-review

Abstract

Let V1, V2, V3, … be a sequence of Q-vector spaces where Vn carries an action of Sn. Representation stability and multiplicity stability are two related notions of when the sequence Vn has a limit. An important source of stability phenomena arises when Vn is the dth homology group (for fixed d) of the configuration space of n distinct points in some fixed topological space X. We replace these configuration spaces with moduli spaces of tuples (W1, …, Wn) of subspaces of a fixed complex vector space CN such that W1 + · · · + Wn = CN. These include the varieties of spanning line configurations which are tied to the Delta Conjecture of symmetric function theory.

Original languageEnglish
Article numberP1.7
JournalElectronic Journal of Combinatorics
Volume30
Issue number1
DOIs
StatePublished - 2023

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