2014/06/05 by Gufang Zhao, Zhao, Gufang, Changlong Zhong +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1406.1283
v2 32 pages, significant modifications
openalex publication_date 2014/06/05 · arxiv created 2015/01/27 · arxiv updated 2015/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung, Malagón-López, 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.