Minimal determining sets for certain W-graph ideals

2021/12/12 by T. P. McDonough, McDonough, T. P., C. A. Pallikaros +1
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2112.06239

openalex publication_date 2021/12/12 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We consider Kazhdan-Lusztig cells of the symmetric group S_n containing the longest element of a standard parabolic subgroup of S_n. Extending some of the ideas in [Beiträge zur Algebra und Geometrie, 59 (2018), no. 3, 523-547] and [Journal of Algebra and Its Applications, 20 (2021), no. 10, 2150181], we determine the rim of some additional families of cells and also of certain induced unions of cells. These rims provide minimal determining sets for certain W-graph ideals introduced in [Journal of Algebra, 361 (2012), 188-212].

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