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  1. ; ; (, The Electronic Journal of Combinatorics)
    Let $$V_1, V_2, V_3, \dots $$ be a sequence of $$\mathbb {Q}$$-vector spaces where $$V_n$$ carries an action of $$\mathfrak{S}_n$$. Representation stability and multiplicity stability are two related notions of when the sequence $$V_n$$ has a limit. An important source of stability phenomena arises when $$V_n$$ is the $$d^{th}$$ 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 $$(W_1, \dots, W_n)$$ of subspaces of a fixed complex vector space $$\mathbb {C}^N$$ such that $$W_1 + \cdots + W_n = \mathbb {C}^N$$. These include the varieties of spanning line configurations which are tied to the Delta Conjecture of symmetric function theory. 
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