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

Authors: Volodymyr Mazorchuk, Rafael Mrđen Journal of Pure and Applied Algebra 224 (2020), Issue 12, 106449 https://doi.org/10.1016/j.jpaa.2020.106449 Abstract: Using translation from the regular block, we construct and analyze properties of BGG complexes in singular blocks of BGG category . We provide criteria, in terms of the Kazhdan-Lusztig-Vogan polynomials, for such complexes to be exact. […]

Author: Rafael Mrđen Mathematical Communications 25(2020), 13–34. https://www.mathos.unios.hr/mc/index.php/mc/article/view/3149 Abstract: Using the Penrose transform, we construct analogues of the BGG (Bernstein-Gelfand-Gelfand) resolutions in certain singular infinitesimal characters, in the holomorphic geometric setting, over the Lagrangian Grassmannian. We prove the exactness of the constructed complex over the big affine cell.

Authors: Dražen Adamović, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše Advances in Mathematics, Volume 360, 22 January 2020, 106918 https://doi.org/10.1016/j.aim.2019.106918 Abstract: This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras [6], [7], [8]. Here we consider conformal embeddings in simple affine vertex superalgebra  where  is a basic classical simple Lie superalgebra. Let  be the subalgebra […]

Authors: Dražen Adamović, Ching Hung Lam, Veronika Pedić, Nina Yu Journal of Algebra, Volume 539, 1 December 2019, Pages 1-23 https://doi.org/10.1016/j.jalgebra.2019.08.007 Abstract: We extend the Dong-Mason theorem on irreducibility of modules for orbifold vertex algebras (cf. [18]) to the category of weak modules. Let V be a vertex operator algebra, g an automorphism of order p. Let W be an irreducible weak V–module such […]