Twisted quadratic foldings of root systems

2018/06/23 by Lanini, Martina, Zainoulline, Kirill
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.08962

Abstract

In the present paper we study twisted foldings of root systems which generalize usual involutive foldings corresponding to automorphisms of Dynkin diagrams. Our motivating example is the Lusztig projection of the root system of type E₈ onto the subring of icosians of the quaternion algebra which gives the root system of type H₄. Using moment graph techniques for any such folding we construct a map at the equivariant cohomology level. We show that this map commutes with characteristic classes and Borel maps. We also introduce and study its restrictions to the usual cohomology of projective homogeneous varieties, to group cohomology and to their virtual analogues for finite reflection groups.

Related

• Twisted quadratic foldings of root systems and liftings of Schubert classes
• Generalized Dynkin diagrams and root systems and their folding
• Root graded groups of type H₃ and H₄
• Structure algebras, Hopf algebroids and oriented cohomology of a group
• Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures