Quantum Schur superalgebras and Kazhdan-Lusztig combinatorics.

DOI10.1016/j.jpaa.2011.03.015zbMath1264.20047arXiv1010.3800OpenAlexW2096697001MaRDI QIDQ640933

Jie Du, Hebing Rui

Publication date: 21 October 2011

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3800

zbMATH Keywords

Schur algebras\(q\)-Schur algebrascanonical basesstandard basesquantum Schur-Weyl dualityRobinson-Schensted-Knuth correspondencecell decompositionsHecke algebras of type \(A\)quantum enveloping superalgebrasquantum matrix superalgebrasquantum Schur superalgebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08) Universal enveloping (super)algebras (17B35) Superalgebras (17A70) Schur and (q)-Schur algebras (20G43)

Related Items (16)

THE QUEER -SCHUR SUPERALGEBRA ⋮ Canonical bases for the quantum supergroup U(𝔤𝔩_3|1) ⋮ Super RSK correspondence with symmetry ⋮ The first and second fundamental theorems of invariant theory for the quantum general linear supergroup ⋮ Cyclotomic q-Schur superalgebras ⋮ A realisation of the quantum supergroup \(U(\mathfrak{gl}_{m|n})\) ⋮ 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 ⋮ Homomorphisms from Specht modules to signed Young permutation modules ⋮ Representations of \(q\)-Schur superalgebras in positive characteristics ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Schur-Weyl reciprocity between the quantum superalgebra and the Iwahori-Hecke algebra
• On Lusztig's isomorphism theorem for Hecke algebras
• Multiparametric quantum deformation of the general linear supergroup
• Cells in certain sets of matrices
• A new proof of the Mullineux conjecture.
• Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
• Cellular algebras
• Robinson-Schensted algorithm and Vogan equivalence
• Symmetric and Exterior Powers, Linear Source Modules and Representations of Schur Superalgebras
• A Double Hall Algebra Approach to Affine Quantum Schur--Weyl Theory
• THE TENSOR ALGEBRA OF THE IDENTITY REPRESENTATION AS A MODULE OVER THE LIE SUPERALGEBRAS $ \mathfrak{Gl}(n,\,m)$ AND $ Q(n)$
• Based algebras and standard bases for quasi-hereditary algebras
• HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA μ_q(gl(m, n))
• Canonical Bases for Irreducible Representations of Quantum GL _n , II
• Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$
• Projective representations of symmetric groups via Sergeev duality

This page was built for publication: Quantum Schur superalgebras and Kazhdan-Lusztig combinatorics.