Quantum queer supergroups via \(\upsilon \)-differential operators

DOI10.1016/j.jalgebra.2022.01.017OpenAlexW4210670228MaRDI QIDQ2118930

Jie Du, Zhongguo Zhou, Ya Nan Lin

Publication date: 23 March 2022

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2022.01.017

zbMATH Keywords

regular representationsupermodulequantum differential operatorquantum queer supergroupqueer \(q\)-Schur superalgebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Rings of differential operators (associative algebraic aspects) (16S32) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Ring-theoretic aspects of quantum groups (16T20) Schur and (q)-Schur algebras (20G43)

Cites Work

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• A realisation of the quantum supergroup \(U(\mathfrak{gl}_{m|n})\)
• Crystal bases for the quantum queer superalgebra
• Quantum queer superalgebra and crystal bases
• A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
• Highest weight modules over quantum queer superalgebra \(U_q(\mathfrak {q}(n))\)
• Quantized universal enveloping superalgebra of type \(Q\) and a super- extension of the Hecke algebra
• Modular representations of the supergroup \(Q(n)\). I
• Polynomial super representations of \(U_q^{\mathrm{res}}(\mathfrak{gl}_{m\mid n})\) at roots of unity
• Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux
• THE TENSOR ALGEBRA OF THE IDENTITY REPRESENTATION AS A MODULE OVER THE LIE SUPERALGEBRAS $ \mathfrak{Gl}(n,\,m)$ AND $ Q(n)$
• THE QUEER -SCHUR SUPERALGEBRA
• The regular representation of 𝑈_{𝜐}(𝔤𝔩_{𝔪|𝔫})
• Presenting Queer Schur Superalgebras
• Projective representations of symmetric groups via Sergeev duality

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