Related papers: Invariant four-forms and symmetric pairs

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We…

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…

Exceptional real groups have quaternionic forms of split rank 4 that contain dual pairs $G\times G'$, where $G'$ is the split Lie group of the type $G_2$, and $G$ a Lie group of split rank one. In this paper we restrict the minimal…

We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\frak{osp}}_{2n|2m}$ with $n\geqslant 2$. We give necessary conditions for an…

A polynomial ring with rational coefficients is an irreducible representation of Lie algebras of endomorphisms of exterior powers of a infinite countable dimensional $\mathbb{Q}$-vector space. We give an explicit description of it, using…

A complete invariant and a binary combination for irreducible representations of SL2(R) are introduced. With this, a new two-parameter family of representations is defined.

In this work we provide an elementary derivation of the indefinite spin groups in low-dimensions. Our approach relies on the isomorphism of Cl(p+1, q+1) to the algebra 2x2 matrices with entries in Cl(p,q), simple properties of Kronecker…

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

This paper is a sequel to arXiv:1401.6321. We define and study representation categories based on Deligne categories Rep(GL_t), Rep(O_t), Rep(Sp_2t), where t is any (non-integer) complex number. Namely, we define complex rank analogs of the…

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…

We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional formulas, Dynkin indices, quadratic Casimir…

By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of…

We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric…

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…

We define natural classes of rational and polynomial representations of the Yangian of the general linear Lie algebra. We also present the classification and explicit realizations of all irreducible rational representations of the Yangian.

We introduce a new way to study representations of the Lie superalgebra $p(n)$. Since the center of the universal enveloping algebra $U$ acts trivially on all irreducible representations, we suggest to study the quotient algebra $\bar{U}$…

We examine unitary and nonunitary representations of the Heisenberg-Weyl Lie algebra $\mathfrak{hw}_n$, with particular emphasis on tensor products of unitary representations and on indecomposable nonunitary representations. In the unitary…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…