Related papers: A Construction of Generalized Harish-Chandra Modul…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…

We construct all finite irreducible modules over Lie conformal superalgebras of type K

We complete the classification of conformal embeddings of a maximally reductive subalgebra $\mathfrak k$ into a simple Lie algebra $\mathfrak g$ at non-integrable non-critical levels $k$ by dealing with the case when $\mathfrak k$ has rank…

In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the unique simple submodule of some tensor module $F(P,V)$ for a simple weight module $P$…

We compute projective dimension of translated simple modules in the regular block of the BGG category $\mathcal{O}$ in terms of Kazhdan-Lusztig combinatorics. This allows us to determine which projectives can appear at the last step of a…

Let g be a exceptional complex simple Lie algebra and q be a parabolic subalgebra. A generalized Verma module M is called a scalar generalized Verma module if it is induced from a one-dimensional representation of q. In this paper, we will…

Let $H(2,1;\underline{t})$ be Hamiltonian superalgebras over $\mathbb{F}$, an algebraically closed field of prime characteristic $p>3$, which are non-restricted simple Lie superalgebras, generally. In this paper, we study generalized…

A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…

Let K be an algebraically closed field. For a graded K-Algebra R, we write cmdef R:=dim R -depth R. We show that for each reductive group G (over K) which is not linearly reductive, there exists a faithful G-module V such that cmdef…

Let ${\mathfrak{g}}$ be a complex semisimple Lie algebra with Borel subalgebra ${\mathfrak{b}}$ and corresponding nilradical ${\mathfrak{n}}$. We show that singular Whittaker modules $M$ are simple if and only if the space $\hbox{Wh}\,M$ of…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with the cocommutative Hopf algebra structure. We show that if L is a primitive Lie pseudoalgebra over H then…

We give a geometric realization of cohomologically induced (g,K)-modules. Let (h,L) be a subpair of (g,K). The cohomological induction is an algebraic construction of (g,K)-modules from a (h,L)-module V. For a real semisimple Lie group, the…

Given a finite-dimensional module, $V$, for a finite-dimensional, complex, semi-simple Lie algebra $\lie g$ and a positive integer $m$, we construct a family of graded modules for the current algebra $\lie g[t]$ indexed by simple $\CC\lie…

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…

Let $n\ge2$ be an integer, $\mathcal{K}_n$ the Weyl algebra over the Laurent polynomial algebra $A_n=\mathbb{C} [x_1^{\pm1}, x_2^{\pm1}, ..., x_n^{\pm1}]$, and $\mathbb{S}_n$ the Lie algebra of divergence zero vector fields on an…

We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple submodule of finite length. This implies that holonomic…

Let $G$ be a connected reductive algebraic group defined over an algebraically closed field %$k$ of characteristic $p > 0$. Our first aim in this note is to give concise and uniform proofs for two fundamental and deep results in the context…

Let $\frak g$ be a semisimple Lie algebra and $\frak k\subset\frak g$ be a reductive subalgebra. We say that a $\frak g$-module $M$ is a bounded $(\frak g, \frak k)$-module if $M$ is a direct sum of simple finite-dimensional $\frak…

Let $G$ be a non-compact classical semisimple Lie group and let $G/V$ be the adjoint orbit with respect to a fixed element in $G$. These manifolds can be equipped with an almost-K\"ahler structure and we provide explicit formulae for the…