On bases for infinite little/infinitesimal \(q\)-Schur algebras
type: Item
instance of: scholarly article
title: On bases for infinite little/infinitesimal \(q\)-Schur algebras
zbMATH Open document ID: 1239.17008
author: Qiang Fu
published in: Archiv der Mathematik
publication date: 2009-11-25T00:00:00Z
review text: Let \(k\) be a field containing a primitive root of unity of order at least 3. The author introduces the infinite little \(q\)-Schur algebra \(u_k(\infty, r)\) over \(k\) as an (infinite-dimensional) subalgebra of the infinite \(q\)-Schur algebra \(S_k(\infty, r)\). Several bases of monomial, Beilinson-Lusztig-MacPherson and PBW type for \(u_k(\infty, r)\) are exhibited. Constructions of bases of monomial and PBW type for the infinite version of the infinitesimal \(q\)-Schur algebra are given.
reviewed by: S. Martin
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G43
zbMATH DE Number: 5638431
zbMATH Keywords: \(q\)-Schur algebras
zbMATH Keywords: infinite little and infinitesimal \(q\)-Schur algebras
zbMATH Keywords: monomial
zbMATH Keywords: BLM and PBW bases
MaRDI profile type: Publication
full work available at URL: s00013-009-0042-3
OpenAlex ID: W2026294076
cites work: A geometric setting for the quantum deformation of \(\mathrm{GL}_n\)
cites work: On the Blocks of the Infinitesimal Schur Algebra
cites work: The q ‐Schur Algebra
cites work: q-Tensor Space and q-Weyl Modules
cites work: Q4781487
cites work: On Infinitesimal Schur Algebras
cites work: Q4861279
cites work: Quantum \(\mathfrak{gl}_\infty\), infinite \(q\)-Schur algebras and their representations
cites work: Infinitesimal quantum \(\mathfrak{gl}_n\) and little \(q\)-Schur algebras
cites work: Linear quivers and the geometric setting of quantum \(\mathrm{GL}_n\).
cites work: Monomial bases for $q$-Schur algebras
cites work: A COMPARISON OF INFINITESIMAL AND LITTLE q-SCHUR ALGEBRAS
cites work: Little \(q\)-Schur algebras at even roots of unity
cites work: Q4029512
cites work: A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
cites work: Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
cites work: Canonical Bases Arising from Quantized Enveloping Algebras
cites work: Some topics on \(GL_ q(n)\)
cites work: On the decomposition matrices of the quantized Schur algebra
DOI: 10.1007/S00013-009-0042-3
description: scientific article; zbMATH DE number 5638431