Representation theory of Lie algebras and Lie superalgebras
Research Output
Articles
Publication Date: 2024
Transformation Groups (1531586X)29(4)pp. 1699-1720
In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that these form a class of not necessarily highest weight modules. We prove that each nonzero level quasi-integrable module is parabolically induced from a cuspidal module, over a finite dimensional Lie superalgebra having a Cartan subalgebra whose corresponding root system just contain real roots; in particular, the classification of nonzero level quasi-integrable modules is reduced to the known classification of cuspidal modules over such Lie superalgebras. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.
Publication Date: 2024
Communications in Algebra (00927872)52(8)pp. 3643-3654
A twisted affine Lie superalgebra is either a twisted affine Lie algebra or of one of the types (Formula presented.) ((Formula presented.) (Formula presented.)), (Formula presented.) or (Formula presented.) ((Formula presented.)). It is known that irreducible integrable highest weight modules over a twisted affine Lie superalgebra of type X do not exist if (Formula presented.) In this paper, we show that nonzero level irreducible integrable finite weight modules over a twisted affine Lie superalgebra of type X do not exist if (Formula presented.). © 2024 Taylor & Francis Group, LLC.
Publication Date: 2023
Publications of the Research Institute for Mathematical Sciences (16634926)59(1)pp. 89-121
In this paper, we complete the characterization of tame irreducible extended affine root supersystems. We give a complete description of tame irreducible extended affine root su-persystems of type X = C(1, 1), C(1, 2), C(2, 2) and BC(1, 1) and determine isomorphic classes. © 2023 Research Institute for Mathematical Sciences, Kyoto University.
Publication Date: 2022
Journal of Algebraic Combinatorics (09259899)55(3)pp. 919-978
Following the definition of a root basis of an affine root system, we define a base of the root system R of an affine Lie superalgebra to be a linearly independent subset B of the linear span of R such that B⊆ R and each root can be written as a linear combination of elements of B with integral coefficients such that either all coefficients are nonnegative or all coefficients are non-positive. Characterization and classification of bases of root systems of affine Lie algebras are known in the literature; in fact, up to ± 1 -multiple, each base of an affine root system is conjugate with the standard base under the Weyl group action. In the super case, the existence of those self-orthogonal roots which are not orthogonal to at least one other root, makes the situation more complicated. In this work, we give a complete characterization of bases of the root systems of twisted affine Lie superalgerbas with nontrivial odd part. We precisely describe and classify them. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
