Related papers: Weight Diagrams of $gl(m|n)$ Modules

The present paper has been motivated by an aspiration for understanding the weight system corresponding to the Lie algebra $\mathfrak{gl}_N$. The straightforward approach to computing the values of a Lie algebra weight system on a general…

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in…

Based on the Kazama-Suzuki type coset construction and its inverse coset between the subregular $\mathcal{W}$-algebras for $\mathfrak{sl}_n$ and the principal $\mathcal{W}$-superalgebras for $\mathfrak{sl}_{1|n}$, we prove weight-wise…

As a homomorphic image of the hyperalgebra $U_{q,R}(m|n)$ associated with the quantum linear supergroup $U_\upsilon(\mathfrak{gl}_{m|n})$, we first give a presentation for the $q$-Schur superalgebra $S_{q,R}(m|n,r)$ over a commutative ring…

In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that quasi-integrable modules are not necessarily highest weight modules. We prove that each quasi-integrable module…

We investigate the representations of the exotic conformal Galilei algebra. This is done by explicitly constructing all singular vectors within the Verma modules, and then deducing irreducibility of the associated highest weight quotient…

Let $V$ be an irreducible representation of group $GL_n({\mathbb C})$, which appears as a submodule in $({\mathbb C}^n)^{\otimes d}$, where ${\mathbb C}^n$ is the tautological $n$-dimensional representation of $GL_n$, and $d$ is a…

According to V. Kac and J. van de Leur, the superconformal algebras are the simple $\Z$-graded Lie superalgebras of growth one which contains the Witt algebra. We describe an explicit classification of all cuspidal modules over the known…

Degenerate modules of the exceptional infinite-dimensional simple Lie superalgebras vle(3|6), ksle(5|10) and mb(3|8) have recently been constructed by Kac and Rudakov, and by Grozman, Leites and Shchepochkina. I rederive their results using…

We consider the foundational problem of maintaining a $(1-\varepsilon)$-approximate maximum weight matching (MWM) in an $n$-node dynamic graph undergoing edge insertions and deletions. We provide a general reduction that reduces the problem…

Let $k$ and $N$ be positive integers with $k\ge2$ even. In this paper we give general explicit upper-bounds in terms of $k$ and $N$ from which all the residual representations $\bar{\rho}_{f,\lambda}$ attached to non-CM newforms of weight…

Methods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y(gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite dimensional…

Let $A_{m,n}$ be the tensor product of the polynomial algebra in $m$ even variables and the exterior algebra in $n$ odd variables over the complex field $\C$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of superderivations…

Let $\mathfrak g$ be either the Lie superalgebra $\mathfrak{gl}(V)\oplus\mathfrak{gl}(V)$ where $V:=\mathbb C^{m|n}$ or the Lie superalgebra $\mathfrak{gl}(V)$ where $V:=\mathbb C^{m|2n}$. Furthermore, let $W$ be the $\mathfrak g$-module…

Let K be an algebraically closed field of characteristic p>0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight…

This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable…

We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of $G$-integrable irreducible highest weight modules over the affine Lie…

In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of…

We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of…

Let G be a linear algebraic group over an algebraically closed field of characteristic p whose corresponding root system is irreducible. In this paper we calculate the Weyl filtration dimension of the induced G-modules, \nabla(\lambda) and…