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Lie Superalgebras and Calogero–Moser–Sutherland Systems
We review recent results obtained at the intersection of the theory of quantum deformed Calogero–Moser–Sutherland systems and the theory of Lie...
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Deformations and generalized derivations of Hom-Lie conformal algebras
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal...
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Minuscule representations and Panyushev conjectures
Recently, Panyushev (2015) raised five conjectures concerning the structure of certain root posets arising from Z-gradings of simple Lie algebras....
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Some properties of generalized reduced Verma modules over ℤ-graded modular Lie superalgebras
We study some properties of generalized reduced Verma modules over ℤ-graded modular Lie superalgebras. Some properties of the generalized reduced...
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Tensor ideals, Deligne categories and invariant theory
We derive some tools for classifying tensor ideals in monoidal categories. We use these results to classify tensor ideals in Deligne’s universal...
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Spectral Characters of a Class of Integrable Representations of Toroidal Lie Algebras
In this paper we study the subcategory of finite-length objects of the category of positive level integrable representations of a toroidal Lie...
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Ordered Tensor Categories and Representations of the Mackey Lie Algebra of Infinite Matrices
We introduce (partially) ordered Grothendieck categories and apply results on their structure to the study of categories of representations of the...
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Limits of Multiplicities in Excellent Filtrations and Tensor Product Decompositions for Affine Kac-Moody Algebras
We express the multiplicities of the irreducible summands of certain tensor products of irreducible integrable modules for an affine Kac-Moody...
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Weyl Modules and Weyl Functors for Lie Superalgebras
Given an algebraically closed field 𝕜 of characteristic zero, a Lie superalgebra 𝔤 over 𝕜 and an associative, commutative 𝕜-algebra A with unit,...
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Differential-operator representations of Weyl group and singular vectors in Verma modules
Given a suitable ordering of the positive root system associated with a semisimple Lie algebra, there exists a natural correspondence between Verma...
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A New Approach to Representations of 3-Lie Algebras and Abelian Extensions
In this paper, we introduce the notion of generalized representation of a 3-Lie algebra, by which we obtain a generalized semidirect product 3-Lie...
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Infinite-dimensional 3-Lie algebras and their connections to Harish-Chandra modules
We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical...
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Whittaker Modules for the Insertion-Elimination Lie Algebra
This paper addresses the representation theory of the insertion-elimination Lie algebra, a Lie algebra that can be naturally realized in terms of...
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Classification of irreducible non-zero level quasifinite modules over twisted affine Nappi-Witten algebra
We obtain that every irreducible quasifinite module with non-zero level over the twisted affine Nappi-Witten algebra is either a highest weight...