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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.


Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young’s seminormal basis
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by Ming Fang, Kay Jin Lim and Kai Meng Tan PDF
Represent. Theory 24 (2020), 551-579 Request permission


Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p>0$, $\Delta (\lambda )$ denote the Weyl module of $G$ of highest weight $\lambda$ and $\iota _{\lambda ,\mu }:\Delta (\lambda +\mu )\to \Delta (\lambda )\otimes \Delta (\mu )$ be the canonical $G$-morphism. We study the split condition for $\iota _{\lambda ,\mu }$ over $\mathbb {Z}_{(p)}$, and apply this as an approach to compare the Jantzen filtrations of the Weyl modules $\Delta (\lambda )$ and $\Delta (\lambda +\mu )$. In the case when $G$ is of type $A$, we show that the split condition is closely related to the product of certain Young symmetrizers and, under some mild conditions, is further characterized by the denominator of a certain Young’s seminormal basis vector. We obtain explicit formulas for the split condition in some cases.
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Additional Information
  • Ming Fang
  • Affiliation: HLM, HCMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China
  • MR Author ID: 715486
  • Email:
  • Kay Jin Lim
  • Affiliation: Division of Mathematical Sciences, Nanyang Technological University, SPMS-04-01, 21 Nanyang Link, 637371 Singapore
  • MR Author ID: 865544
  • ORCID: 0000-0002-2605-0482
  • Email:
  • Kai Meng Tan
  • Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076 Singapore
  • MR Author ID: 656415
  • Email:
  • Received by editor(s): December 12, 2019
  • Received by editor(s) in revised form: July 20, 2020, and August 24, 2020
  • Published electronically: October 29, 2020
  • Additional Notes: The first author was supported by NSFC (No. 11688101, 11471315 and 11321101), while the second and third authors were supported by Singapore MOE Tier 2 AcRF MOE2015-T2-2-003.
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 551-579
  • MSC (2020): Primary 20G05, 20C30
  • DOI:
  • MathSciNet review: 4168181