Related papers: Symmetrizers for Schur superalgebras

Over the $(1,n)$-dimensional real supercircle, we consider the $\mathcal{K}(n)$-modules of linear differential operators, $\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie…

In the first part of the article we introduce $C^*$-algebras associated to self-similar groups and study their properties and relations to known algebras. The algebras are constructed as sub-algebras of the Cuntz-Pimsner algebra (and its…

We develop a pseudo-differential approach to the N=2 supersymmetric unconstrained matrix (k|n,m)-Generalized Nonlinear Schroedinger hierarchies and prove consistency of the corresponding Lax-pair representation (nlin.SI/0201026).…

We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing…

The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…

The Schur $\mathsf{Lie}$-multiplier of Leibniz algebras is the Schur multiplier of Leibniz algebras defined relative to the Liezation functor. In this paper, we study upper bounds for the dimension of the Schur $\mathsf{Lie}$-multiplier of…

Let M_0=G_0/H be a (n+1)-dimensional Cahen-Wallach Lorentzian symmetric space associated with a symmetric decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation r:H->GL_R(S) of the stabilizer H. This…

We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and…

We consider a filtration of the symmetric function space given by $\Lambda^{(k)}_t$, the linear span of Hall-Littlewood polynomials indexed by partitions whose first part is not larger than $k$. We introduce symmetric functions called the…

Let $\mathrm{JT}_\lambda$ be the Jacobi-Trudi matrix corresponding to the partition $\lambda$, so $\det\mathrm{JT}_\lambda$ is the Schur function $s_\lambda$ in the variables $x_1,x_2,\dots$. Set $x_1=\cdots=x_n=1$ and all other $x_i=0$.…

We review the algebraic approach to super non-Abelian T-Duality considered in [1], focusing on symmetric and semi-symmetric coset spaces on $G/H$. We discuss a potential impediment, appearing in these models when integrating out the gauge…

We construct and analyze dual N=4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the…

The linear (homogeneous and inhomogeneous) (k, N, N-k) supermultiplets of the N-extended one-dimensional Supersymmetry Algebra induce D-module representations for the N=2,4,8 superconformal algebras. For N=2, the D-module representations of…

The supersymmetric completion of higher-derivative operators often requires introducing corrections to the scalar potential. In this paper we study these corrections systematically in the context of theories with $\mathcal{N}=1$ global and…

We establish a connection between a generalization of KLR algebras, called quiver Schur algebras, and the cohomological Hall algebras of Kontsevich and Soibelman. More specifically, we realize quiver Schur algebras as algebras of…

We consider the space of differential operators $\mathcal{D}_{\lambda\mu}$ acting between $\lambda$- and $\mu$-densities defined on $S^{1|2}$ endowed with its standard contact structure. This contact structure allows one to define a…

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights.…

In this paper, new sequence spaces $X(r, s, t ;\Delta^{(m)})$ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator of order $m$ are introduced. It is shown that these spaces are complete normed linear…

We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers $S_M$ on Schatten $p$-classes which solves a conjecture proposed by Mikael de la Salle. Given $1 < p < \infty$, a simple form our main result…

A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parameterise the SL(N,R)/SO(N)…