Work

Higher spin representations of maximal compact subalgebras of simply-laced Kac-Moody-algebras

Year: 2024

Type: article

Abstract: Given the maximal compact subalgebra $\mathfrak{k}(A)$ of a split-real Kac-Moody algebra $\mathfrak{g}(A)$ of type $A$, we study certain finite-dimensional representations of $\mathfrak{k}(A)$, that do not lift to the maximal compact subgroup $K(A)$ of the minimal Kac-Moody group $G(A)$ associated to $\mathfrak{g}(A)$ but only to its spin cover $Spin(A)$. Currently, four elementary of these so-called spin representations are known. We study their (ir-)reducibility, semi-simplicity, and lift to the group level. The interaction of these representations with the spin-extended Weyl-group is used to derive a partial parametrization result of the representation matrices by the real roots of $\mathfrak{g}(A)$.

Source: URN:NBN Resolver for Germany & Switzerland (German National Library)

DOI: 10.48550/arxiv.2409.07247

Authors: Lautenbacher, Robin, Köhl, Ralf

Institution: Christian-Albrechts-Universität zu Kiel

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Studienstiftung des Deutschen Volkes

OpenAlex ID: W7127918403

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