Proudfoot, Nicholas; Young, Ben Configuration spaces, \(\mathrm{FS}^{\mathrm{op}}\)-modules, and Kazhdan-Lusztig polynomials of braid matroids. (English) Zbl 1475.55018 New York J. Math. 23, 813-832 (2017). Summary: The equivariant Kazhdan-Lusztig polynomial of a braid matroid may be interpreted as the intersection cohomology of a certain partial compactification of the configuration space of \(n\) distinct labeled points in \(\mathbb C\), regarded as a graded representation of the symmetric group \(S_n\). We show that, in fixed cohomological degree, this sequence of representations of symmetric groups naturally admits the structure of an \(\mathrm{FS}\)-module, and that the dual \(\mathrm{FS}^{\mathrm{op}}\)-module is finitely generated. Using the work of Sam and Snowden [Zbl 1347.05010], we give an asymptotic formula for the dimensions of these representations and obtain restrictions on which irreducible representations can appear in their decomposition. Cited in 10 Documents MSC: 55R80 Discriminantal varieties and configuration spaces in algebraic topology 55N33 Intersection homology and cohomology in algebraic topology 20C30 Representations of finite symmetric groups Keywords:configuration space; representation stability; Kazhdan-Lusztig polynomial Citations:Zbl 1347.05010 PDFBibTeX XMLCite \textit{N. Proudfoot} and \textit{B. Young}, New York J. Math. 23, 813--832 (2017; Zbl 1475.55018) Full Text: arXiv EMIS