The question is motivated by a more broad perspective in another MO post and here, but here we would like to understand a specific case (our question potentially connects to / is motivated by Wess–Zumino–Witten_model and Non-linear $\sigma$ model and Quantum Gravity), Question: We would like to ...

Is well know that given a semi-simple (or simple) Lie group $G$, then any derivation $\delta : \frak{g}\to\frak{g}$ of the Lie algebra $\frak{g}$ is inner, i.e. $\delta(X)={\rm ad}(X)$ for any $X\in\frak{g}$, where ${\rm ad} : \frak{g}\to {\rm End}(\frak{g})$ is the adjoint representation of $\fr...

Suppose we are given an algebraic group $G$ (linearly reductive). Let $D^b(Repr(G))$ be the bounded derived category of finite dimensional algebraic representations of $G$. I am intressted in tilting objects for this category. Is there something known...some reference or articles treating this pr...

Let $G$ be a connected, simply-connected complex semisimple group. Let $$\mathcal{G}r:=G((t))/G[[t]]$$ be its affine Grassmannian. I have read that $\mathcal{G}r$ possesses a natural very ample line bundle/invertible sheaf (see "A Polytope Calculus for Semisimple Groups" by J. Anderson, for insta...