Graded Cartan determinants of the symmetric groups

Tsuchioka, Shunsuke

doi:10.1090/S0002-9947-2013-05916-8

Graded Cartan determinants of the symmetric groups
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Trans. Amer. Math. Soc. 366 (2014), 2019-2040 Request permission

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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