Related papers: Equivariant map queer Lie superalgebras

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…

We consider a real Abelian Lie supergroup $G$ acting on its complexification $M$, equipped with a $G$-invariant super K\"ahler form. We extend the scheme of classical geometric quantization to this setting and construct a unitary…

We say that an indecomposable Cartan matrix A with entries in the ground field of characteristic 0 is almost affine if the Lie sub(super)algebra determined by it is not finite dimensional or affine but the Lie (super)algebra determined by…

For G a finite group and X a G-space on which a normal subgroup A acts trivially, we show that the G-equivariant K-theory of X decomposes as a direct sum of twisted equivariant K-theories of X parametrized by the orbits of the conjugation…

We classify the finite dimensional irreducible representations of rectangular finite $W$-algebras, i.e., the finite $W$-algebras $U(\mathfrak{g}, e)$ where $\mathfrak{g}$ is a symplectic or orthogonal Lie algebra and $e \in \mathfrak{g}$ is…

Given a finite vector space $V=\mathbb{F}_q^n$, the $q$-analogue of a graph, called a $q$-graph, is a pair $\Gamma=(\mathcal{V},\mathcal{E})$, where $\mathcal{V}$ is the set of $1$-dimensional subspaces of $V$ and $\mathcal{E}$ is a subset…

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…

For a Lie algebra ${\mathcal L}$ with basis $\{x_1,x_2,\cdots,x_n\}$, its associated characteristic polynomial $Q_{{\mathcal L}}(z)$ is the determinant of the linear pencil $z_0I+z_1\text{ad} x_1+\cdots +z_n\text{ad} x_n.$ This paper shows…

A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with {\em any} finite dimensional unitary irrep for these…

We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective…

We study the manifold $Q_{\Gamma, \lambda}$ of isospectral real skew-symmetric matrices with a prescribed sparsity pattern determined by a graph $\Gamma$. The compact torus $T^n$ acts naturally on $Q_{\Gamma,\lambda}$ by conjugation, and…

Let $\bbcq$ be the quantum torus associated with the $d \times d$ matrix $q = (q_{ij})$, $q_{ii} = 1$, $q_{ij}^{-1} = q_{ji}$, $q_{ij}$ are roots of unity, for all $1 \leq i, j \leq d.$ Let $\Der(\bbcq)$ be the Lie algebra of all the…

We develop a reduction procedure which provides an equivalence from an arbitrary block of the BGG category for the queer Lie superalgebra $\mathfrak{q}(n)$ to a "$\mathbb{Z}\pm s$-weights" ($s\in \mathbb{C}$) block of a BGG category for…

A class of highest weight irreducible representations of the algebra $U_h(A_\infty)$, the quantum analogue of the completion and central extension $A_\infty$ of the Lie algebra $gl_\infty$, is constructed. It is considerably larger than the…

The goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups. This concerns the following notions and results: the…

Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are…

In this article we construct link invariants and 3-manifold invariants from the quantum group associated with Lie superalgebra $\mathfrak{sl}(2|1)$. This construction based on nilpotent irreducible finite dimensional representations of…

In the present paper we classify all irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type S. The classification is based on a bijective correspondence between the continuous representations of the…

Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…

Let $\mathfrak{g}=\mathfrak{gl}_{M|N}(\mathbb{k})$ be the general linear Lie superalgebra over an algebraically closed field $\mathbb{k}$ of characteristic zero. Fix an arbitrary even nilpotent element $e$ in $\mathfrak{g}$ and let…