Schur-Weyl duality for infinitesimal q-Schur algebras s(q)(2, r)(1) - Erdmann, K; Fu, Q (Elsevier, 2008)
Using the result of [S.R. Doty, D.K. Nakano, K.M. Peters, Polynomial representations of Frobenius kernels of GL, in: Contemp. Math., vol. 194, 1996, pp. 57-67; S. König, C. Xi, When is a cellular algebra quasi-hereditary? Math. Ann. 315 (1999) 281-293], we prove that a non-semisimple infinitesimal Schur algebra s (2, r) is not cellular. Furthermore, we determine the structure of the endomorphism ring of tensor space as a module for the infinitesimal Schur algebra s (2, r), up to Morita equivalence. Both results generalize to the quantum case. © 2008 Elsevier Inc. All rights reserved.