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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An integral second fundamental theorem of invariant theory for partition algebras
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by Chris Bowman, Stephen Doty and Stuart Martin
Represent. Theory 26 (2022), 437-454
DOI: https://doi.org/10.1090/ert/593
Published electronically: April 1, 2022

Abstract:

We prove that the kernel of the action of the group algebra of the Weyl group acting on tensor space (via restriction of the action from the general linear group) is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra over an arbitrary commutative ring and proves that the centraliser algebras of the partition algebra are cellular. We also prove similar results for the half partition algebras.
References
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Bibliographic Information
  • Chris Bowman
  • Affiliation: Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom
  • MR Author ID: 922280
  • Email: Chris.Bowman-Scargill@york.ac.uk
  • Stephen Doty
  • Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60660
  • MR Author ID: 59395
  • ORCID: 0000-0003-3927-3009
  • Email: doty@math.luc.edu
  • Stuart Martin
  • Affiliation: DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
  • MR Author ID: 270122
  • ORCID: 0000-0002-7424-8397
  • Email: S.Martin@dpmms.cam.ac.uk
  • Received by editor(s): October 28, 2018
  • Received by editor(s) in revised form: July 5, 2021
  • Published electronically: April 1, 2022
  • Additional Notes: The first author was supported by funding from EPSRC fellowship grant EP/V00090X/1.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 437-454
  • MSC (2020): Primary 20C30, 20G05, 20C20
  • DOI: https://doi.org/10.1090/ert/593
  • MathSciNet review: 4403137