Global crystal bases and q-Schur algebras

DOI10.1142/S0219498815501170zbMath1356.17016OpenAlexW2057589930MaRDI QIDQ5255739

Anna Stokke

Publication date: 19 June 2015

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498815501170

zbMATH Keywords

quantum groupYoung tableau\(q\)-Schur algebraglobal crystal basisCarter-Lusztig basis

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Schur and (q)-Schur algebras (20G43)

Cites Work

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• A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
• A combinatorial description of the quantum Désarménien matrix via the \(q\)-Schur algebra
• Dual canonical bases and Kazhdan-Lusztig polynomials
• Quantum deformation of flag schemes and Grassmann schemes. I: A \(q\)- deformation of the shape-algebra for \(GL(n)\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Standard basis theorem for quantum linear groups
• Codeterminants and \(q\)-Schur algebras.
• A quantum version of the Désarménien matrix.
• Quantum GL_n
• The q ‐Schur Algebra
• A SIMPLE ALGORITHM FOR COMPUTING THE GLOBAL CRYSTAL BASIS OF AN IRREDUCIBLE U_q(sl_n)-MODULE
• An Algorithm to Compute the Canonical Basis of an Irreducible Module Over a Quantized Enveloping Algebra

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