Oriented cohomology rings of semisimple groups admit finite presentations via formal Demazure operators; explicit minimal presentations are given for adjoint and simply-connected groups of types A1, A2, B2.
Title resolution pending
2 Pith papers cite this work, alongside 12 external citations. Polarity classification is still indexing.
2
Pith papers citing it
12
external citations · OpenAlex
abstract
For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung, Malag\'on-L\'opez, Savage, and Zainoulline. Coming from this formal group law, there is also an oriented cohomology theory. We identify the formal affine Hecke algebra with a convolution algebra coming from the oriented cohomology theory applied to the Steinberg variety. As a consequence, this algebra acts on the corresponding cohomology of the Springer fibers. This generalizes the action of classical affine Hecke algebra on the $K$-theory of the Springer fibers constructed by Lusztig. We also give a residue interpretation of the formal affine Hecke algebra, which coincides with the residue construction of Ginzburg, Kapranov, and Vasserot when the formal group law comes from a 1-dimensional algebraic group.
years
2026 2representative citing papers
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
citing papers explorer
-
A technique for computing oriented cohomology rings of semisimple algebraic groups
Oriented cohomology rings of semisimple groups admit finite presentations via formal Demazure operators; explicit minimal presentations are given for adjoint and simply-connected groups of types A1, A2, B2.
-
Motivic Segre classes of Schubert cells and the connective formal group law
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.