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The affine vertex superalgebra of D(2,1;-v/w) at level 1

  • Author / Creator
    Stockall, Devon
  • The affine vertex superalgebra A=L^1(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;a) is an extension of the direct sum of 3 copies of sl(2),  A can be naturally realized as an extension of L_1=L^k(sl(2))x L^l(sl(2))x L^1(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 L_1 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 L^(k-1)(sl(2))x B^l, where the SVOA B^l is constructed from a `half-lattice' and L^1(sl(2)).  This allows calculation of modular S-matrices for A modules induced from relaxed highest weight L_1 modules.  
    

  • Subjects / Keywords
  • Graduation date
    Fall 2023
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-rcb5-gg69
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.