A criterion for quasi-hereditary, and an abstract straightening formula |
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Authors: | Steffen König |
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Institution: | 1. Fakult?t für Mathematik, Universit?t Bielefeld, Postfach 10 01 31, D-33501, Bielefeld, Germany
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Abstract: | A criterion is given to show that a –algebra is quasi–hereditary if it can be defined over an integral domain , and if there is a certain commutative semisimple subalgebra satisfying a technical but easily verified condition (which
roughly states that over the field of fractions of , the formal characters of the semisimple –algebra generated by the –algebra defining satisfy an ordering condition). This applies in particular to Schur algebras (where various proofs of quasi–hereditary are
known, by de Concini, Eisenbud and Procesi, by Donkin, by Parshall, and by J.A. Green), generalized Schur algebras (covering
a result of Donkin), –Schur algebras (Dipper and James, Parshall and Wang), and Temperley–Lieb algebras (Westbury). The second application of this
point of view is an abstract straightening formula for the algebras satisfying the assumptions of the first theorem.
Oblatum 27-III-1995 & 18-IV-1996 |
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Keywords: | |
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