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Mathematics > Representation Theory

arXiv:1807.07457 (math)
[Submitted on 19 Jul 2018 (v1), last revised 23 Aug 2018 (this version, v3)]

Title:Type A-admissible cells are Kazhdan-Lusztig

Authors:Van Minh Nguyen
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Abstract:Admissible W-graphs were defined and combinatorially characterised by Stembridge in reference [12]. The theory of admissible W-graphs was motivated by the need to construct W-graphs for Kazhdan-Lusztig cells, which play an important role in the representation theory of Hecke algebras, without computing Kazhdan-Lusztig polynomials. In this paper, we shall show that type A-admissible W-cells are Kazhdan-Lusztig as conjectured by Stembridge in his original paper.
Comments: 40 pages, correction to the proof for Case 1 of Lemma 7.29. (iv) Comment added in introduction: Magma file available on request
Subjects: Representation Theory (math.RT); Group Theory (math.GR)
MSC classes: 20C08, 20C30
Cite as: arXiv:1807.07457 [math.RT]
  (or arXiv:1807.07457v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1807.07457

Submission history

From: Van Nguyen [view email]
[v1] Thu, 19 Jul 2018 14:16:27 UTC (54 KB)
[v2] Fri, 3 Aug 2018 06:31:24 UTC (55 KB)
[v3] Thu, 23 Aug 2018 03:14:33 UTC (55 KB)
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