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Quiver Grassmannians for the Bott-Samelson resolution of type A Schubert varieties (2502.11790v2)
Published 17 Feb 2025 in math.RT, math.AG, and math.CO
Abstract: We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a \textit{geometrically compatible} decomposition for any permutation in $S_n$. For smooth type A Schubert varieties, we identify a suitable dimension vector such that the corresponding quiver Grassmannian is isomorphic to the Schubert variety. To obtain these isomorphisms, we construct a special quiver with relations and investigate two classes of quiver Grassmannians for this quiver.