Year: 2026
Type: preprint
Abstract: Let $G$ be the affine Kac--Moody group of type $\widetilde A_{n-1}$, $B$ be an Iwahori subgroup in $G$, $\mathcal{F}=G/B$ be the flag variety, and $W$ be the Weyl group of $G$. Given distinct involutions $w_1$, $w_2\in W$, we prove that the tangent cones $C_{w_1}$, $C_{w_2}$ to the corresponding Schubert subvarieties $X_{w_1}$ and $X_{w_2}$ of $\mathcal{F}$ at the point $p=e\mod B$ do not coincide as subvarieties of the tangent space to $\mathcal{F}$ at the point $p$. This generalizes similar results in the finite-dimensional setting. The main technical tools we used are combinatorics of the embeddings of the Weyl groups of different ranks and coadjoint orbits for the unipotent radical of the group $B$.
Source: arXiv (Cornell University)
Authors: Bondar, Stepan, Ignatev, Mikhail
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203726822
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