Master's thesis
Devon Stockall
University of Alberta, 2023
University of Alberta, 2023
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APA
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Stockall, D. (2023). The affine vertex algebra of D(2,1;-v/w) at level 1 (Master's thesis). University of Alberta.
Chicago/Turabian
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Stockall, Devon. “The Affine Vertex Algebra of D(2,1;-v/w) at Level 1.” Master's thesis, University of Alberta, 2023.
MLA
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Stockall, Devon. The Affine Vertex Algebra of D(2,1;-v/w) at Level 1. University of Alberta, 2023.
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@mastersthesis{devon2023a,
title = {The affine vertex algebra of D(2,1;-v/w) at level 1},
year = {2023},
school = {University of Alberta},
author = {Stockall, Devon},
howpublished = {}
}
The affine vertex superalgebra A= L1(D(2,1;−v/w)) plays a key role as the geometric Langlands kernel VOA for SVOAs associated to so(3), osp(1|2) and other rank one Lie superalgbras. Since D(2,1; α) is an extension of the direct sum of 3 copies of sl(2), A can be naturally realized as an extension of L1 =Lk(sl(2))xLl(sl(2))xL1(sl(2)) for admissible levels k=u/v−2 and l=u/w−2. Here, I use constructions of gluing VOAs to realize A as an L1 extension, and the theory of VOA extensions to classify irreducible modules in A-wtmod≥0. Using the ‘Adamovic procedure’, an alternate realization of A is given as a subalgebra of Lk−1(sl(2))xBl, where the SVOA Bl is constructed from a ‘half-lattice’ and L1(sl(2)). This allows calculation of modular S-matrices for A modules induced from relaxed highest weight L1 modules.