Related papers: Signature Characters for A_2 and B_2

Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with residue field of odd characteristic, $\mathfrak{p}$ be its maximal ideal and let $\mathfrak{o}_\ell = \mathfrak{o}/\mathfrak{p}^\ell$ for $\ell\ge 2$. In this…

In this paper, the correspondence between the finite dimensional representations of a simple Lie algebra and their characteristic polynomials is established, and a monoid structure on these characteristic polynomials is constructed.…

We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional…

We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive…

Let G be the real points of a simply connected, semisimple, simply laced complex Lie group, and let \tilde{G} be the nonlinear double cover of G. We discuss a set of small genuine irreducible representations of \tilde{G} which can be…

We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of representation…

In the first part of the paper we give the denominator identity for all simple finite-dimensional Lie super algebras $\frak g\/$ with a non-degenerate invariant bilinear form. We give also a character and (super) dimension formulas for all…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

We study properties and constructions of contravariant forms on reduction algebras. As an application we compute norms of highest weight vectors in the tensor product of an irreducible finite dimensional representation of the Lie algebra…

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg's type II classical graded Lie algebras.

For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

Let $G$ be a connected semisimple simply connected Lie group with a compact Cartan subgroup and let $\Gamma$ be a uniform lattice in $G$. Let $\widehat{G}_d$ denote the set of equivalence classes of unitary discrete series representations…

We study a class of algebras B(n,l) associated with integrable models with boundaries. These algebras can be identified with coideal subalgebras in the Yangian for gl(n). We construct an analog of the quantum determinant and show that its…

Let L be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic p>3. We prove in this paper that if all tori of maximal dimansion in the semisimple p-envelope of L are standard, the L is up to…

The multiplicities a_{lambda,mu} of simple modules L(mu) in the composition series of Kac modules V(lambda) for the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character problem for gl(m/n). In…

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…

In a recent paper, V. Dobrev and A. Sudbery classified the highest-weight and lowest-weight finite dimensional irreducible representations of the quantum Lie algebra sl(2)_q introduced by V. Lyubashenko and A. Sudbery. The aim of this note…

We describe the isomorphism classes of certain infinite-dimensional graded Lie algebras of maximal class, generated by an element of weight one and an element of weight two, over fields of odd characteristic.

We use recent results of Rolen, Zwegers, and the first author to study characters of irreducible (highest weight) modules for the vertex operator algebra $L_{\frak{sl}_\ell}(-\Lambda_0)$. We establish asymptotic behaviors of characters for…