Conference abstracts
Session S08 - Lie Groups and Representations
July 28, 15:40 ~ 16:20
Representation ring of Levi subgroups versus cohomology ring of flag varieties
Shrawan Kumar
University of North Carolina, Chapel Hill, USA - kumar@math.unc.edu
Recall the classical result that the cup product structure constants for the singular cohomology with integral coefficients of the Grassmannian of r-planes coincide with the Littlewood-Richardson tensor product structure constants for GL(r). Specifically, the result asserts that there is an explicit ring homomorphism ϕ:Reppoly(GL(r))→H∗(Gr(r,n)), where Gr(r,n) denotes the Grassmannian of r-planes in Cn and Reppoly(GL(r)) denotes the polynomial representation ring of GL(r).
This work seeks to achieve one possible generalization of this classical result for GL(r) and the Grassmannian Gr(r,n) to the Levi subgroups of any reductive group G and the corresponding flag varieties.