Multiplication formulas and isomorphism theorem of $\imath$Schur superalgebras

Jian Chen; Li Luo

Multiplication formulas and isomorphism theorem of $\imath$Schur superalgebras

Representation Theory 2022-09-20 v2 Quantum Algebra

Authors: Jian Chen , Li Luo

Abstract

We introduce the notion of $\imath$ Schur 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 $\imath$ Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the $\imath$ Scuhr superalgebras and the $q$ -Schur superalgebras of type A, which helps us derive a semisimplicity criteria of the $\imath$ Schur superalgebras.

Keywords

schur superalgebra hecke algebra canonical basis isomorphism theorem semisimplicity type b/c type a

Cite

@article{arxiv.2202.02564,
  title  = {Multiplication formulas and isomorphism theorem of $\imath$Schur superalgebras},
  author = {Jian Chen and Li Luo},
  journal= {arXiv preprint arXiv:2202.02564},
  year   = {2022}
}

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v2, 39 pages, minor edit

Multiplication formulas and isomorphism theorem of $\imath$Schur superalgebras

Abstract

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