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Let $G$ be a real semisimple Lie group, $K$ be a maximal compact subgroup. Let $\mathfrak{g}_0$ and $\mathfrak{k}_0$ be their real Lie algebras respectively. Let $\mathfrak{g}$ and $\mathfrak{k}$ be ...

Fix $G$ a finite dimensional reductive group and $\lambda$ a weight. Apparently the category of $\mathcal{D}_\lambda$ modules on $G/B$ is equivalent to the category of $\mathcal{D}_0$ modules on $G'/B'...

This is question is about whether or not certain modules for an affine Lie algebra are generated by their singular vectors. I begin with some background. Backround on affine Lie algebras. Let $\...

Nakajima has constructed so-called reflection functors that are isomorphisms between different quiver varieties that have the same framing $\mathbf{w}:$ $$\Phi_{\sigma}:\mathfrak{M}_\zeta(Q,\mathbf{v}...

Let $G$ be a connected reductive group over $\mathbb{C}$ of Lie algebra $\mathfrak{g}$. What is the value of $H^{3}(\mathfrak{g}((t))((s)),\mathbb{C})$?

Given a decomposition $p=(p_1,\dots,p_n)$ of $n$, one can associate its corresponding partial flag variety $$\mathcal{B}_p=\{F=(0=F_0\subset F_1\subset \dots \subset F_n=\mathbb{C}^n) \mid \dim F_i/F_{...