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Graded Cartan determinants of the symmetric groups


Author: Shunsuke Tsuchioka
Journal: Trans. Amer. Math. Soc. 366 (2014), 2019-2040
MSC (2010): Primary 81R50; Secondary 20C08
DOI: https://doi.org/10.1090/S0002-9947-2013-05916-8
Published electronically: December 6, 2013
MathSciNet review: 3152721
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Abstract: We give the graded Cartan determinants of the symmetric groups. Based on that, we propose a gradation of Hill's conjecture which is equivalent to Külshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.


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Additional Information

Shunsuke Tsuchioka
Affiliation: Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, the University of Tokyo, Kashiwa, Japan 277-8583
Email: tshun@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-2013-05916-8
Keywords: Symmetric groups, Iwahori-Hecke algebras, graded representation theory, quantum groups, Shapovalov forms, quiver Hecke algebras, generalized blocks
Received by editor(s): June 5, 2012
Received by editor(s) in revised form: June 13, 2012, and July 3, 2012
Published electronically: December 6, 2013
Additional Notes: This research was supported by Grant-in-Aid for Research Activity Startup 22840026 and Research Fellowships for Young Scientists 23$⋅$8363, Japan Society for the Promotion of Science
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.