Minimal determining sets for certain W-graph ideals

Thomas P. McDonough; Christos A. Pallikaros

doi:10.22108/ijgt.2022.131838.1764

Minimal determining sets for certain W-graph ideals

Thomas P. McDonough
, Christos A. Pallikaros^*

^*Corresponding author for this work

Department of Mathematics

University of Cyprus

Research output: Contribution to journal › Article › peer-review

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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].

Original language	English
Pages (from-to)	123-151
Number of pages	29
Journal	International Journal of Group Theory
Volume	12
Issue number	3
Early online date	21 Nov 2022
DOIs	https://doi.org/10.22108/ijgt.2022.131838.1764
Publication status	Published - 01 Sept 2023

Keywords

Kazhdan-Lusztig cell
reduced form
W-graph ideal

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title = "Minimal determining sets for certain W-graph ideals",

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AU - Pallikaros, Christos A.

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N2 - We consider Kazhdan-Lusztig cells of the symmetric group Sn containing the longest element of a standard parabolic subgroup of Sn. 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].

AB - We consider Kazhdan-Lusztig cells of the symmetric group Sn containing the longest element of a standard parabolic subgroup of Sn. 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].

KW - Kazhdan-Lusztig cell

KW - reduced form

KW - W-graph ideal

UR - https://www.scopus.com/pages/publications/85141387540

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DO - 10.22108/ijgt.2022.131838.1764

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VL - 12

SP - 123

EP - 151

JO - International Journal of Group Theory

JF - International Journal of Group Theory

IS - 3

ER -

Minimal determining sets for certain W-graph ideals

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