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For a semisimple complex Lie algebra $\mathfrak{g}$ and a regular element $X\in \mathfrak g$ the centralizer of $X$ in $\mathfrak g$ is a Cartan subalgebra (see Knapp, 'Lie Groups beyond an ...

In the paper titled Equivariant (K-)homology of affine Grassmannian and Toda lattice, the authors, Roman Bezrukavnikov, Michael Finkelberg, and Ivan Mirković, derived the coordinate ring of each ...

In $G=\operatorname{PGL}_{2n}(\textbf{C})$, WLG, we assume all the toral elementary abelian 2-subgroups in discussion are in $T$, the image in $G$ of the group of diagonal matrices in $\operatorname{...

$\DeclareMathOperator\GL{GL}$If $G$ is a simple Lie group, and $\rho: G \to \GL(V)$ is a representation, then by Schur's lemma, the group of automorphisms of $\rho$ is a reductive subgroup of $\GL(V)$....