Related papers: Combinatorial aspects of the linkage principle for…

The purpose of the paper is to derive formulas that describe the structure of the induced supermodule H^0_G(\la) for the general linear supergroup G=GL(m|n) over an algebraically closed field K of characteristic p\neq 2. Using these…

Let $G=GL(m|n)$ be the general linear supergroup over an algebraically closed field $K$ of characteristic zero and let $G_{ev}=GL(m)\times GL(n)$ be its even subsupergroup. The induced supermodule $H^0_G(\lambda)$, corresponding to a…

In this note we determine when is an induced module H^0_G(\lambda), corresponding to a dominant integral highest weight \lambda of the general linear supergroup G=GL(m|n) irreducible. Using the contravariant duality given by the supertrace…

We consider a generalization of Donkin-Koppinen filtrations for coordinate superalgebras of general linear supergroups. More precisely, if $G=GL(m|n)$ is a general linear supergroup of (super)degree $(m|n)$, then its coordinate superalgebra…

For a general linear supergroup $G=GL(m|n)$, we consider a natural isomorphism $\phi: G \to U^-\times G_{ev} \times U^+$, where $G_{ev}$ is the even subsupergroup of $G$, and $U^-$, $U^+$ are appropriate odd unipotent subsupergroups of $G$.…

We prove the linkage principle and describe blocks of the general linear supergroups $GL(m|n)$ over the ground field $K$ of characteristic $p\neq 2$.

This paper provides results on the modular representation theory of the supergroup $GL(m|n).$ Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation…

Let $\boldsymbol{\Lambda}\,(=\mathbb{F}^{n^{3}})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|>2$, be the space of structure vectors of algebras having the $n$-dimensional $\mathbb{F}$-space $V$ as the underlying vector space. Also let…

We introduce a family $\mathbb{M}_{r;f,\eta}$ of infinitesimal supergroup schemes, which we call multiparameter supergroups, that generalize the infinitesimal Frobenius kernels $\mathbb{G}_{a(r)}$ of the additive group scheme…

This work was inspired by two natural questions. The first question is when Lie(G')=Lie(G)', where G is a connected algebraic supergroup defined over a field of characteristic zero. The second question is whether the unipotent radical of…

Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on…

Let $G$ be a group hyperbolic relative to a collection of subgroups $\{H_\lambda ,\lambda \in \Lambda \} $. We say that a subgroup $Q\le G$ is hyperbolically embedded into $G$, if $G$ is hyperbolic relative to $\{H_\lambda ,\lambda \in…

We initiate the study of subgroups $H$ of the general linear group $GL_{\binom{n}{m}}(R)$ over a commutative ring $R$ that contain the $m$-th exterior power of an elementary group $\bigwedge^mE_n(R)$. Each such group $H$ corresponds to a…

The paper contains results that characterize the Donkin-Koppinen filtration of the coordinate superalgebra $K[G]$ of the general linear supergroup $G=GL(m|n)$ by its subsupermodules $C_{\Gamma}=O_{\Gamma}(K[G])$. Here, the supermodule…

We develop a fragment of the theory of Duflo-Serganova functor over a field of odd characteristic. We elaborate a method of computing the symmetry supergroup $\widetilde{\mathbb{G}_x}$ of this functor, recently introduced by A.Sherman, for…

Let $g$ be a finite-dimensional simple Lie algebra over the complex number field. We classify the homomorphisms between $g$-modules induced from one-dimensional modules of maximal parabolic subalgebras.

Many properties of simple finite dimensional gl(m|n)-modules may be better understood by assigning weight diagrams to the highest weights with respect to a given base of simple roots. In this paper we consider bases that are compatible with…

Description of adjoint invariants of general Linear Lie superalgebras $\mathfrak{gl}(m|n)$ by Kantor and Trishin is given in terms of supersymmetric polynomials. Later, generators of invariants of the adjoint action of the general linear…

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of type $A_\ell^{(1)}$. Suppose we're given a $\mathbb Z$-gradation of the corresponding simple finite-dimensional Lie algebra ${\mathfrak g}={\mathfrak g}_{-1}\oplus{\mathfrak g}_0 \oplus…

Let $q$ be a prime power, $G=GL_n(q)$ and let $U\leqslant G$ be the subgroup of (lower) unitriangular matrices in $G$. For a partition $\lambda$ of $n$ denote the corresponding unipotent Specht module over the complex field $\C$ for $G$ by…