Large-dimensional homomorphism spaces between Weyl modules and Specht modules. (Q1946085)

The author gives a family of pairs of Weyl modules for the \(q\)-Schur algebras for which the corresponding homomorphsm space is at least \(2\)-dimensional. As an application, she shows that there exist arbitrarily large homomorphism spaces between pairs of Weyl modules with any choices of roots of unity \(q\neq 1\) or with \(q=1\) and over a positive characteristic ground field \(F\).