Demazure Modules, Chari-Venkatesh Modules and Fusion Products

Symmetry Integrability and Geometry-Methods and Applications

article

Bhimarthi Ravinder¹ 

[1] The Institute of Mathematical Sciences

关键词: current algebra;    Demazure module;    Chari–Venkatesh module;    truncated Weyl module;    fusion product;   

DOI  :  10.3842/SIGMA.2014.110

来源: National Academy of Science of Ukraine

【 摘 要 】

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$. Given two non-negative integers $m$, $n$, we prove that the fusion product of $m$ copies of the level one Demazure module $D(1,\theta)$ with $n$ copies of the adjoint representation ${\rm ev}_0 V(\theta)$ is independent of the parameters and we give explicit defining relations. As a consequence, for $\mathfrak{g}$ simply laced, we show that the fusion product of a special family of Chari-Venkatesh modules is again a Chari-Venkatesh module. We also get a description of the truncated Weyl module associated to a multiple of $\theta$.

【 授权许可】

Unknown