Related papers: Reduction method for representations of queer Lie …

We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category O for a general linear Lie…

We establish a maximal parabolic version of the Kazhdan-Lusztig conjecture \cite[Conjecture 5.10]{CKW} for the BGG category $\mathcal{O}_{k,\zeta}$ of $\mathfrak{q}(n)$-modules of "$\pm \zeta$-weights", where $k\leq n$ and…

Block type Lie algebras have been studied by many authors in the latest twenty years. In this paper, we will study a class of more general Block type Lie algebra $\mathcal{B}(p,q)$, which is a class of infinite-dimensional Lie algebra by…

We describe all blocks of the category of finite-dimensional $\mathfrak{q}(3)$-supermodules by providing their extension quivers. We also obtain two general results about the representation of $\mathfrak{q}(n)$: we show that the Ext quiver…

We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules.…

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

We apply the super duality formalism recently developed by the authors to obtain new equivalences of various module categories of general linear Lie superalgebras. We establish the correspondence of standard, tilting, and simple modules, as…

For a field $F$ of characteristic zero and an additive subgroup $G$ of $F$, a Lie algebra $B(G)$ of lock type is defined with basis $\{L_{a,i},c|a \in G, i>-2\}$ and relations…

We study various categories of Whittaker modules over the queer Lie superalgebras $\mathfrak q(n)$. We formulate standard Whittaker modules and reduce the problem of composition factors of these standard Whittaker modules to that of Verma…

We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique…

In this paper we classify all simple weight modules for a quantum group $U_q$ at a complex root of unity $q$ when the Lie algebra is not of type $G_2$. By a weight module we mean a finitely generated $U_q$-module which has finite…

An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power…

In the theory of finite groups, the irreducible representations of G over a field F are classified into blocks based on a direct decompositions of the group algebra FG. This gives a natural decomposition of FG-modules into direct summands,…

A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup…

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional…

Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$, we establish an equivalence between parabolic BGG categories of a Kac-Moody Lie superalgebra and a Kac-Moody Lie algebra. The characters for a…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) $X$ to a queer Lie superalgebra $\mathfrak{q}$ that are equivariant with respect to the action of a finite group…

Let $\mathfrak{g}$ be a reductive Lie algebra over an algebraically closed, characteristic zero field or over $\mathbb{R}$. Let $\mathfrak{q}$ be a parabolic subalgebra of $\mathfrak{g}$. We characterize the derivations of $\mathfrak{q}$ by…

We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements.…