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

Leader: Prof. Pavle Pandžić

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A note on principal subspaces of the affine Lie algebras in types B_l^{(1)}, C_l^{(1)}, F_4^{(1)} and G_2^{(1)}

Thursday August 27th, 2020 Rafael Mrđen 0

Author: Marijana Butorac Communications in Algebra, doi: 10.1080/00927872.2020.1788046 Abstract: We construct quasi-particle bases of principal subspaces of standard modules , where , and  denotes the fundamental weight of affine Lie algebras of type , or of level one. From the given bases we find characters of principal subspaces. Keywords: Affine Lie algebras, combinatorial bases, principal subspaces, quasi-particles, vertex operator algebras

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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.

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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 […]