Mathematics > Representation Theory
[Submitted on 22 Apr 2018]
Title:The Z_2 Orbifold of the Universal Affine Vertex Algebra
View PDFAbstract:Let $\gg$ be a simple, finite-dimensional complex Lie algebra, and let $V^k(\gg)$ denote the universal affine vertex algebra associated to $\gg$ at level $k$. The Cartan involution on $\gg$ lifts to an involution on $V^k(\gg)$, and we denote by $V^k(\gg)^{\mathbb{Z}_2}$ the orbifold, or fixed-point subalgebra, under this involution. Our main result is an explicit minimal strong finite generating set for $V^k(\gg)^{\mathbb{Z}_2}$ for generic values of $k$. In the case $\gg = \gs\gl_2$, we also determine the set of nongeneric values of $k$, where this set does not work.
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