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Simple modules for the partition algebra and monotone convergence of kronecker coefficients

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Publication details

JournalInternational Mathematics Research Notices
DateAccepted/In press - 6 Apr 2017
DateE-pub ahead of print - 11 Jul 2017
DatePublished (current) - 1 Feb 2019
Issue number4
Volume2019
Number of pages39
Pages (from-to)1059-1097
Early online date11/07/17
Original languageEnglish

Abstract

We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone convergence property for Kronecker coefficients using stratifications of the cell modules of the partition algebra.

Bibliographical note

Funding Information:
The authors are grateful for the financial support received from the Royal Commission for the

Funding Information:
Exhibition of 1851 and EPSRC grant EP/L01078X/1.

Publisher Copyright:
© The Author(s) 2017.

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