Leader: Prof. Pavle Pandžić

BGG complexes in singular blocks of category O

Wednesday May 20th, 2020 Rafael Mrđen 0

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. […]

Singular BGG complexes for the symplectic case

Wednesday March 11th, 2020 Rafael Mrđen 0

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.

Conformal embeddings in affine vertex superalgebras

Wednesday November 27th, 2019 Rafael Mrđen 0

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 […]

On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras

Thursday August 22nd, 2019 Rafael Mrđen 0

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 […]

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