Standard Homological Properties for Quantum GLn

✍ Scribed by Stephen Donkin

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 379 KB
• Volume: 181
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0118

✦ Synopsis

DEDICATED TO ROGER W. CARTER ON THE OCCASION OF HIS 60TH BIRTHDAY

For some time, we have been studying Schur algebras and related w x algebras by a technique of descent from algebraic groups 9᎐13 . In the case of a Schur algebra, one can then, by a further technique of descent Ž w x . described in 17, Chap. 6 , go on to study the group algebra of the corresponding symmetric group. The main inputs from algebraic group theory are the various homological properties of the induction functor G Ž . Ind where G is a reductive group with Borel subgroup B , particularly B Kempf's vanishing theorem. It is often difficult or awkward to realize the consequences of these properties directly within the context of finite dimensional algebras. We now wish to study the q-Schur algebra, introw x duced by Dipper and James 6 , and Hecke algebras of type A, in a similar manner by descent from quantum GL .