Symplectomorphism group of $T^*(G_\mathbb{C}/B)$ and the braid group I: a homotopy equivalence for $G_\mathbb{C}=SL_3(\mathbb{C})$

TL;DR

This paper establishes a homotopy equivalence between the symplectomorphism group of the cotangent bundle of the flag variety and the braid group for the case of $SL_3(\

Contribution

It proves a homotopy equivalence for the symplectomorphism group and the braid group specifically for $SL_3(\

Findings

Homotopy equivalence between symplectomorphism group and braid group for $SL_3(\

paper_type":"theoretical"}}

Abstract

For a semisimple Lie group $G_\mathbb{C}$ over $\mathbb{C}$, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups in the case of $G_\mathbb{C}=SL_3(\mathbb{C})$, under the $SU(3)$-equivariancy condition on symplectomorphisms.