Geodesic
Singularities of Schubert Varieties within a Right Cell
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe an algorithm which pattern embeds, in the sense of Woo–Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan–Lusztig cell. This apparently harmless fact has applications in finding examples of reducible associated varieties of $\mathfrak{sl}_n$-highest weight modules, as well as in the study of $W$-graphs for symmetric groups, and in comparing various bases of irreducible representations of the symmetric group or its Hecke algebra. For example, we are able to systematically produce many negative answers to a question from the 1980s of Borho–Brylinski and Joseph, which had been settled by Williamson via computer calculations only in 2014.
Keywords: Schubert varieties, interval pattern embedding
Mots-clés : Kazhdan–Lusztig cells, Specht modules. 
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     author = {Martina Lanini and Peter J. McNamara},
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Martina Lanini; Peter J. McNamara. Singularities of Schubert Varieties within a Right Cell. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a69/

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