Schur Algebras of Classical Groups II

Abstract

We study Schur algebras of classical groups over an algebraically closed field of characteristic different from 2. We prove that Schur algebras are generalized Schur algebras (in Donkin's sense) in types A, C, and D, while this does not hold in type B. Consequently Schur algebras of types A, C, and D are integral quasi-hereditary by Donkin [7, 9]. By using the coalgebra approach we put Schur algebras of a fixed classical group into a certain inverse system. We find that the corresponding hyperalgebra is contained in the inverse limit as a subalgebra. Moreover in types A, C, and D, the surjections in the inverse systems are compatible with the integral quasi-hereditary structure of Schur algebras.

Key Words:

• Classical group
• Generalized Schur algebra
• Hyperalgebra
• Inverse system
• Schur algebra

2000 Mathematics Subject Classification:

• Primary 20G05
• Secondary 16D90

ACKNOWLEDGMENTS

The author acknowledges support by the AsiaLink network Algebras and Representations in China and Europe, ASI/B7-301/98/679-11, and by the Leverhulme Trust through the Academic Interchange Network Algebras, Representations and Applications.

Notes

Communicated by C. Cibils.