Multiplication formulas and isomorphism theorem of ıSchur superalgebras

Jian Chen; Li Luo

doi:10.1016/j.jpaa.2022.107229

Multiplication formulas and isomorphism theorem of ıSchur superalgebras

Jian Chen, Li Luo

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce the notion of ıSchur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ıSchur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ıScuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ıSchur superalgebras.

Original language	English
Article number	107229
Journal	Journal of Pure and Applied Algebra
Volume	227
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2022.107229
State	Published - Mar 2023

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abstract = "We introduce the notion of ıSchur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ıSchur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ıScuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ıSchur superalgebras.",

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AB - We introduce the notion of ıSchur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ıSchur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ıScuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ıSchur superalgebras.

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Multiplication formulas and isomorphism theorem of ıSchur superalgebras

Abstract

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