Crystals for Kostant-Kumar modules of $\widehat{\mathfrak{sl}_2}$

Mrigendra Singh Kushwaha, K. N. Raghavan, Sankaran Viswanath
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Abstract

We consider the affine Lie algebra $\widehat{\mathfrak{sl}_2}$ and the Kostant-Kumar submodules of tensor products of its level 1 highest weight integrable representations. We construct crystals for these submodules in terms of the charged partitions model and describe their decomposition into irreducibles.
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$\widehat\mathfrak{sl}_2}$ 的 Kostant-Kumar 模块晶体
我们考虑了仿射李代数 $\widehat{\mathfrak{sl}_2}$ 及其第 1 层最高权重可整合表示的张量积的科斯坦特-库马尔子模块。我们用带电分区模型来构造这些子模子的晶体,并描述它们被分解成irreducibles的情况。
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