相关论文: Kostant's problem for parabolic Verma modules

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

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 classify the irreducible modules for the fixed point vertex operator subebra of the rank 1 free bosonic VOA under the -1 automorphism.

Using translation from the regular block, we construct and analyze properties of BGG complexes in singular blocks of BGG category ${\mathcal{O}}$. We provide criteria, in terms of the Kazhdan-Lusztig-Vogan polynomials, for such complexes to…

This article supplements recent work of the authors. (1) A criterion for failure of covariant finiteness of a full subcategory of $\Lambda\text{-mod}$ is given, where $\Lambda$ is a finite dimensional algebra. The criterion is applied to…

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

Assuming the Lusztig conjecture on the irreducible characters for reductive algebraic groups in positive characteristic $p$, which is now a theorem for large $p$, we show that the modules for their Frobenius kernels induced from the simple…

In this paper, we find an explicit combinatorial criterion for the existence of a nonzero GL_{n-1}(K)-high weight vector of weight (\lambda_1,...,\lambda_{i-1},\lambda_i-d,\lambda_{i+1},..., \lambda_{n-1}), where d<char K and K is an…

We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of projective space as a…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of representations of the conformal algebra induced from the maximal cuspidal parabolic.

We present a relationship between the Calogero-Moser particles confined in harmonic oscillator potentials and a representation theory of the infinite dimensional Lie algebra which is a semi-direct sum of Virasoro algebra and its module.…

Zhao and the second author (2013) constructed a functor from o(k)-Mod to o(k + 2)-Mod. In this paper, we use the functor successively to obtain an universal first-order differential operator realization for any highest-weight representation…

Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula…

In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the…

We examine the structure of the Levi component $MA$ in a minimal parabolic subgroup $P = MAN$ of a real reductive Lie group $G$ and work out the cases where $M$ is metabelian, equivalently where $\mathfrak{p}$ is solvable. When $G$ is a…

We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although this result is in principle known, the…

In this paper we define the degree of a morphism between (generalized) Verma modules over a graded Lie superalgebra and construct series of morphisms of various degrees between (generalized) Verma modules over the exceptional…

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…

Lowest weight representations of the ${\mathbb Z}_2 \otimes {\mathbb Z}_2$ graded superalgebra introduced by Rittenberg and Wyler are investigated. We give a explicit construction of Verma modules over the ${\mathbb Z}_2 \otimes {\mathbb…

We investigate representations of the $\mathbb{Z}_2^2$-graded extension of $osp(1|2)$ which is the spectrum generating algebra of the recently introduced $\mathbb{Z}_2^2$-graded version of superconformal mechanics. The main result is a…