Monomial bases for $q$-Schur algebras

DOI10.1090/S0002-9947-02-03188-4zbMath1023.17006MaRDI QIDQ4787476

Brian J. Parshall, Jie Du

Publication date: 7 January 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

quantized enveloping algebraHecke algebramonomial basiscanonical basisPBW-basis\(q\)-Schur algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08) Representation theory for linear algebraic groups (20G05)

Related Items (25)

Little \(q\)-Schur algebras at even roots of unity ⋮ Canonical bases for modified quantum \(\mathfrak{gl}_n\) and \(q\)-Schur algebras ⋮ Linear quivers and the geometric setting of quantum \(\mathrm{GL}_n\). ⋮ On 0-Schur algebras. ⋮ Unnamed Item ⋮ Presenting integral q-Schur algebras ⋮ The BLM realization for the integral form of \(U_v(\mathfrak{gl}_{m\mid n})\) ⋮ Presenting cyclotomic q-Schur algebras ⋮ A COMPARISON OF INFINITESIMAL AND LITTLE q-SCHUR ALGEBRAS ⋮ Presenting affine Schur algebras ⋮ The infinitesimal and the little q-Schur superalgebras ⋮ Representation type of the little \(q\)-Schur algebras ⋮ Quantum $$\mathfrak{gl}_n,$$ q-Schur Algebras and Their Infinite/Infinitesimal Counterparts ⋮ Monomial bases for quantum affine \(\mathfrak{sl}_n\) ⋮ Infinitesimal quantum \(\mathfrak{gl}_n\) and little \(q\)-Schur algebras ⋮ Quantum \(\mathfrak{gl}_\infty\), infinite \(q\)-Schur algebras and their representations ⋮ On Schur algebras and little Schur algebras ⋮ Monomial Bases for Little q-Schur Algebras s(2,r) ⋮ Monomial base for little \(q\)-Schur algebra \(u_k(2,r)\) at even roots of unity ⋮ Monomial Bases for Littleq-Schur Algebras at Even Roots of Unity ⋮ Polynomial super representations of \(U_q^{\mathrm{res}}(\mathfrak{gl}_{m\mid n})\) at roots of unity ⋮ Presenting q-Schur algebras as quotients of the quantized enveloping algebra of sln ⋮ On bases for infinite little/infinitesimal \(q\)-Schur algebras ⋮ The center of q-Schur algebra U(2,r) ⋮ Presenting Little q-Schur Algebras u_k(2; r)

Cites Work

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• A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Hecke algebras of type \(A_ n\) and subfactors
• \(q\)-Schur algebras as quotients of quantized enveloping algebras
• Representations of Coxeter groups and Hecke algebras
• 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 \(\mathfrak g\mathfrak l_n\)
• Presenting Schur algebras as quotients of the universal enveloping algebra of \(\mathfrak{gl}_2\).
• \(q\)-Schur algebras, asymptotic forms, and quantum \(SL_ n\)
• On degenerations and extensions of finite dimensional modules
• Bases of quantized enveloping algebras
• Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
• Canonical Bases Arising from Quantized Enveloping Algebras
• The q ‐Schur Algebra
• q-Tensor Space and q-Weyl Modules
• Based algebras and standard bases for quasi-hereditary algebras
• Geometric construction of the global base of the quantum modified algebra of \(\hat{\mathfrak g}{\mathfrak l}_N\)

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