Chennai Mathematical Institute


3.15 pm, Seminar Hall
Cotangent Bundle to the Partial Flag Variety

Rahul Singh
Northeastern University, USA.


Let $\widehat{SL}_n$ be the affine Kac-Moody group associated to the simple group $SL_n$. Let $P$ (resp. $\mathcal P$) be the parabolic subgroup of $SL_n$ (resp. $\widehat {SL}_n$) corresponding to the choice of simple roots $\alpha_1,\ldots,\alpha_d$. For $P$ a maximal proper subgroup of $SL_n$ and \Para\ the corresponding parabolic subgroup of \gLhat, Lakshmibai has shown that there is an affine Schubert variety in $\gLhat/\mathcal P$ which is a natural compactification of the cotangent bundle $T^*G/P$. In this talk, we partially extend this result to all parabolic subgroups $P$. In particular, we construct an embedding $\phi_P:T^*G/P\hookrightarrow\gLhat/\Para$ and identify the minimal $\kappa$ for which $\image{\phi_P}\subset X_\Para(\kappa)$. The closure of $\image(\phi_P)$ in $X_\Para(\kappa)$ is then a \gl-stable compactification of $T^*\gl/P$. This is joint work with Lakshmibai.