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Motives of reductive groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 1, February 2012
- pp. 235-257
- 10.1353/ajm.2012.0005
- Article
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Our aim is to prove that the geometric motive with rational coefficients of a split reductive
group $G$ over a perfect field decomposes as the symmetric co-algebra object of certain split mixed
Tate motives which are computable in terms of the root data of $G$. Moreover the isomorphism respects
the Hopf algebra structures in a weight graded sense. We will also provide explicit decompositions in
the case of classical groups.