TL;DR
This paper introduces the cyclotomic q-Schur superalgebra, explores its structure as a cellular superalgebra, and establishes a Schur-Weyl duality with the cyclotomic Hecke algebra, advancing the understanding of superalgebra representations.
Contribution
It defines the cyclotomic q-Schur superalgebra via permutation supermodules and proves its cellularity and duality with the cyclotomic Hecke algebra.
Findings
Cyclotomic q-Schur superalgebra is a cellular superalgebra.
Established Schur-Weyl duality between the superalgebra and cyclotomic Hecke algebra.
Provides structural insights into superalgebra representations.
Abstract
The paper aims to introduce the cyclotomic -Schur superalgebra via the permutation supermodules of the cyclotomic Hekce algebra and investigate its structure. In particular, we show that the cyclotomic -Schur superalgebra is a cellular superalgebra and establish the Schur-Weyl duality between the cyclotomic Hecke algebra and the cyclotomic -Schur superalgebra.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics