Little q-Schur algebras at even roots of unity

In [J. Du, Q. Fu, J.-P. Wang, Infinitesimal quantum and little q-Schur algebras, J. Algebra 287 (2005) 199–233], little q-Schur algebras were introduced as homomorphic images of infinitesimal quantum in the odd root of unity case. In this paper, we shall introduce little q-Schur algebras uk(n,r) at even roots of unity. We shall construct various bases for uk(n,r) and give the dimension formula of uk(n,r).