On bases for infinite little/infinitesimal \(q\)-Schur algebras
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.
infinite little and infinitesimal \(q\)-Schur algebras
scientific article; zbMATH DE number 5638431
scientific article