A COMPARISON OF INFINITESIMAL AND LITTLE q-SCHUR ALGEBRAS

DOI10.1081/AGB-200064357zbMath1179.20043OpenAlexW2088972033MaRDI QIDQ5699898

Qiang Fu

Publication date: 27 October 2005

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

Full work available at URL: https://doi.org/10.1081/agb-200064357

zbMATH Keywords

Schur algebrascohomologyrepresentationsmonomial basesFrobenius kernelsquantized enveloping algebrasfinite general linear groupslittle \(q\)-Schur algebrasinfinitesimal \(q\)-Schur algebrasPBW-type bases

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10) Schur and (q)-Schur algebras (20G43)

Related Items (15)

Little \(q\)-Schur algebras at even roots of unity ⋮ Presenting affine infinitesimal Schur algebras ⋮ Tame representation type of infinitesimal \(q\)-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 ⋮ Infinitesimal quantum \(\mathfrak{gl}_n\) and little \(q\)-Schur algebras ⋮ On Schur algebras and little Schur algebras ⋮ 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 ⋮ On the hyperalgebra of the loop algebra \(\hat{\mathfrak{gl}}_n\) ⋮ On bases for infinite little/infinitesimal \(q\)-Schur algebras ⋮ The Cartan Matrix of Littleq-Schur Algebrau_q(2,r) ⋮ On the structure of ${\rm End}_{u_k(2)}(\Omega _k^{\otimes r})$ End uk(2)(Ωk⊗r) ⋮ Presenting Little q-Schur Algebras u_k(2; r)

Cites Work

• A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
• A two-parameter quantization of GL(n)
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Some topics on \(GL_ q(n)\)
• Infinitesimal quantum \(\mathfrak{gl}_n\) and little \(q\)-Schur algebras
• The modular representation theory of \(q\)-Schur algebras. II
• Quantum GL_n
• Two-Parameter Quantum Linear Groups and the Hyperbolic Invariance of q -Schur Algebras
• The q ‐Schur Algebra
• Monomial bases for $q$-Schur algebras
• On Infinitesimal Schur Algebras

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