Quantum $$\mathfrak{gl}_n,$$ q-Schur Algebras and Their Infinite/Infinitesimal Counterparts

DOI10.1007/978-0-8176-4697-4_5zbMath1242.17015OpenAlexW126690502MaRDI QIDQ3015530

Qiang Fu, Jie Du

Publication date: 13 July 2011

Published in: Representation Theory of Algebraic Groups and Quantum Groups (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-8176-4697-4_5

zbMATH Keywords

quantum groupinfinite \(q\)-Schur algebraquantum Schur algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35) Simple, semisimple, reductive (super)algebras (17B20) Schur and (q)-Schur algebras (20G43)

Cites Work

• A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
• Little \(q\)-Schur algebras at even roots of unity
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Representations of Coxeter groups and Hecke algebras
• Hall algebras and quantum groups
• Some topics on \(GL_ q(n)\)
• Quantum Weyl reciprocity and tilting modules
• Linear quivers and the geometric setting of quantum \(\mathrm{GL}_n\).
• Aperiodicity in quantum affine \(\mathfrak g\mathfrak l_n\)
• Infinitesimal quantum \(\mathfrak{gl}_n\) and little \(q\)-Schur algebras
• Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
• Canonical Bases Arising from Quantized Enveloping Algebras
• Monomial bases for $q$-Schur algebras
• On Infinitesimal Schur Algebras
• A COMPARISON OF INFINITESIMAL AND LITTLE q-SCHUR ALGEBRAS
• Introduction to quantum groups
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