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A Tensor 2-Product of 2-Representations of $\Mathfrak{sl}_{2}^{+}$ by McMillan, Matthew is a scholarly article available to read on EtoBox.

What is A Tensor 2-Product of 2-Representations of $\Mathfrak{sl}_{2}^{+}$ about?

We construct an explicit abelian model for the operation of tensor $2$-product of $2$-representations of $\mathfrak{sl}_{2}^{+}$, specifically the product of a simple $2$-representation $\mathcal{L}(1)$ with a given abelian $2$-representation $\mathcal{V}$ taken from the $2$-category of algebras. We study the case $\mathcal{V}=\mathcal{L}(1)$ in detail, and we show that the $2$-product in this case recovers the expected structure. Our construction partially verifies a conjecture of Rouquier from 2008.

Author

McMillan, Matthew

Published

2022

Language

EN