For example, let $\mathfrak{g}=\mathfrak{sl}_{2}\left(\mathbb{C}\right)$, let $s_{0}=1$, $s_{1}=-1$, $s_{2}$=0, $s_{3}=\infty$ in $\mathbb{P}_{1}\left(\mathbb{C}\right)$ and $\mathcal{R}$ is the algebra of meromorphic functions over $\mathbb{P}_{1}\left(\mathbb{C}\right)$ with possible poles in $s_{i},0\le i\le3$.

Let $V$ be a fundamental 2-dimensional representation of $\mathfrak{g}$ and $V^{\prime}=V\otimes\mathbb{C}\left(\left(t\right)\right)$.

I wish to study $\mathfrak{g}\otimes\mathcal{R}$-modules over $V^{\prime}\otimes V^{\prime}$.

I would appreciate a reference for construction and use of $\mathfrak{g}\otimes\mathcal{R}$.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy