Unit for Representation Theory of Lie Algebras, Number Theory, and Related Structures

Author: Dražen Adamović Communications in Mathematical Physics, pp 1–43 https://doi.org/10.1007/s00220-019-03328-4 Abstract: We study the embeddings of the simple admissible affine vertex algebras and , into the tensor product of rational Virasoro and N = 1 Neveu–Schwarz vertex algebra with lattice vertex algebras. By using these realizations we construct a family of weight, […]

Authors: Butorac Marijana, Sadowski Christopher New York Journal of Mathematics, Volume 25 (2019), 71-106 http://nyjm.albany.edu/j/2019/25-3.html Abstract: We construct combinatorial bases of principal subspaces of standard modules of level with highest weight for the twisted affine Lie algebras of type , , and . Using these bases we directly calculate characters of […]

Authors: Mirko Primc, Tomislav Šikić The Ramanujan Journal, pp 1–35. https://doi.org/10.1007/s11139-018-0052-5 Abstract: In this paper, we give a combinatorial parametrization of leading terms of defining relations for the vacuum level  standard modules for the affine Lie algebra of type . Using this parametrization, we conjecture colored Rogers–Ramanujan type combinatorial identities for  and ; the identity […]

Authors: Dražen Adamović, Victor G Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše International Mathematics Research Notices, rny237, https://doi.org/10.1093/imrn/rny237 Abstract: We discover a large class of simple affine vertex algebras , associated to basic Lie superalgebras  at non-admissible collapsing levels , having exactly one irreducible -locally finite module in the category . In the case when  is […]