Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 110, 10 pages      arXiv:1409.0274      https://doi.org/10.3842/SIGMA.2014.110
Contribution to the Special Issue on New Directions in Lie Theory

Demazure Modules, Chari-Venkatesh Modules and Fusion Products

Bhimarthi Ravinder
The Institute of Mathematical Sciences, CIT campus, Taramani, Chennai 600113, India

Received September 11, 2014, in final form December 01, 2014; Published online December 12, 2014

Abstract
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 $\theta$.

Key words: current algebra; Demazure module; Chari-Venkatesh module; truncated Weyl module; fusion product.

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