Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose we are given an algebraic group $G$ (linearly reductive). Let $D^b(Repr(G))$ be the bounded derived category of finite dimensional algebraic representations of $G$. I am intressted in tilting objects for this category. Is there something known...some reference or articles treating this problem?

share|improve this question
    
The category is semisimple --- just take the sum of all simple representations. –  Sasha Dec 29 '13 at 12:40
    
Ok. But the number of these simple representations may be infinite right? Are there some nontrivial tilting objects known for certain groups? –  Aleksa Dec 29 '13 at 12:58
    
If the number of simple objects is infinite, then there is no finite dimensional tilting generator (for any finite dimensional representation there is a simple object which is not its summand and so it is in the orthogonal). –  Sasha Dec 29 '13 at 14:05
    
Do you assume the tilting object is a finite dimensional representation...I mean the tilting object could be a komplex in $D^b(Repr(G))$... So what is when $G$ is not assumed to be linearly reductive? –  Aleksa Dec 29 '13 at 14:47
1  
The book of Jantzen is a good starting point. –  Sasha Dec 29 '13 at 15:25

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.