A realisation of the quantum supergroup \(U(\mathfrak{gl}_{m|n})\)

DOI10.1016/j.jalgebra.2013.12.034zbMath1316.17010OpenAlexW12114555MaRDI QIDQ401625

Jie Du, Haixia Gu

Publication date: 27 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2013.12.034

zbMATH Keywords

quantum superalgebraHecke algebraSchur-Weyl reciprocity\(q\)-Schur superalgebraquantum supergrouptensor superspace

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08) Superalgebras (17A70) Quantum groups (quantized function algebras) and their representations (20G42) Schur and (q)-Schur algebras (20G43)

Related Items (15)

The integral Schur-Weyl-Sergeev duality ⋮ THE QUEER -SCHUR SUPERALGEBRA ⋮ Canonical bases for the quantum supergroup U(𝔤𝔩_3|1) ⋮ Canonical bases for the quantum supergroups \(\mathbf U(\mathfrak{gl}_{m|n})\) ⋮ Irreducible representations of \(q\)-Schur superalgebras at a root of unity. ⋮ The BLM realization for the integral form of \(U_v(\mathfrak{gl}_{m\mid n})\) ⋮ The infinitesimal and the little q-Schur superalgebras ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Representations of \(q\)-Schur superalgebras in positive characteristics ⋮ The regular representation of 𝑈_{𝜐}(𝔤𝔩_{𝔪|𝔫}) ⋮ MULTIPLICATION FORMULAS AND SEMISIMPLICITY FOR -SCHUR SUPERALGEBRAS ⋮ Polynomial super representations of \(U_q^{\mathrm{res}}(\mathfrak{gl}_{m\mid n})\) at roots of unity ⋮ Multiplication formulas and isomorphism theorem of \({\imath}\)Schur superalgebras ⋮ A REALIZATION OF THE ENVELOPING SUPERALGEBRA ⋮ Quantum queer supergroups via \(\upsilon \)-differential operators

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