We show that the signed p-Kostka numbers depend just on p-Kostka numbers and the multiplicities of projective indecomposable modules in certain signed Young permutation modules. We then examine the signed p-Kostka number k(α|β),(λ|pμ) in the case when |β|=p|μ|. This allows us to explicitly describe the multiplicities of direct summands of a signed Young permutation module lying in the principal block of FSmp in terms of the p-Kostka numbers.
On signed p-Kostka matrices / Giannelli E.; Lim K.J.. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 225:(2021), pp. 1-21. [10.1016/j.jpaa.2020.106631]
On signed p-Kostka matrices
Giannelli E.;
2021
Abstract
We show that the signed p-Kostka numbers depend just on p-Kostka numbers and the multiplicities of projective indecomposable modules in certain signed Young permutation modules. We then examine the signed p-Kostka number k(α|β),(λ|pμ) in the case when |β|=p|μ|. This allows us to explicitly describe the multiplicities of direct summands of a signed Young permutation module lying in the principal block of FSmp in terms of the p-Kostka numbers.
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