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 $\phi: \text{Rep}_{poly}(GL(r)) \to H^*(Gr(r, n))$, where $Gr(r, n)$ denotes the Grassmannian of $r$-planes in $\mathbb{C}^n$ and $\text{Rep}_{poly} (GL(r))$ 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.