F. Marko

activity

20092020

most citedIrreducibility of induced modules for general linear supergroups

5 citations · 5 across the 11 of their papers we have counts for

collaborators

17 papers

math.RT2020

A combinatorial approach to Donkin-Koppinen filtrations of general linear supergroups

Frantisek Marko

For a general linear supergroup $G = G L (m ∣ n)$ , we consider a natural isomorphism $ϕ : G \to U^{-} \times G_{e v} \times U^{+}$ , where $G_{e v}$ is the even subsupergroup of $G$ , and $U^{-}$ , $…

math.RA2020

Symmetrizers for Schur superalgebras

Frantisek Marko

For the Schur superalgebra $S = S (m ∣ n, r)$ over a ground field $K$ of characteristic zero, we define symmetrizers $T^{λ} [i : j]$ of the ordered pairs of tableaux $T_{i}, T_{j}$ of the shape $…

math.NT2020

A note on the geometry of figurate numbers

Frantisek Marko

We give a short proof of the formula $n^{p} = \sum_{ℓ = 0}^{p - 1} (- 1)^{ℓ} c_{p, ℓ} F_{n}^{p - ℓ}$ , where $F_{n}^{p - ℓ}$ is the figurate number and $c_{p, ℓ}$ is the number of $(…

math.RT2018

Central elements in the distribution algebra of a general linear supergroup and supersymmetric elements

Frantisek Marko, Alexandr N. Zubkov

In this paper we investigate the image of the center $Z$ of the distribution algebra $D i s t (G L (m ∣ n))$ of the general linear supergroup over a ground field of positive characteristic…

math.RA2018

Supersymmetric elements in divided powers algebras

Frantisek Marko

Description of adjoint invariants of general Linear Lie superalgebras $gl (m ∣ n)$ by Kantor and Trishin is given in terms of supersymmetric polynomials. Later, generators…

math.RT2016

Combinatorial aspects of the linkage principle for general linear supergroups

Frantisek Marko

Let $G = G L (m ∣ n)$ be a general linear supergroup and $G_{e v}$ be its even subsupergroup isomorphic to $G L (m) \times G L (n)$ . In this paper we use the explicit description of $G_{e v}$ -p…

math.RT2016

Minimal degrees of invariants of (super)groups - a connection to cryptology

Frantisek Marko, Alexandr N. Zubkov

We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public…

math.RT2016

Linkage principle for ortho-symplectic supergroups

Frantisek Marko, Alexandr N. Zubkov

The purpose of the paper is to derive linkage principle for modular representations of ortho-symplectic supergroups. We follow the approach of Doty and investigate in detail the re…

math.RT2016

Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebras

Frantisek Marko

Let $G = G L (m ∣ n)$ be the general linear supergroup over an algebraically closed field $K$ of characteristic zero and let $G_{e v} = G L (m) \times G L (n)$ be its even subsupergroup. The ind…

math.RT2015

Blocks for general linear supergroup $G L (m ∣ n)$

Frantisek Marko, Alexandr N. Zubkov

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

cs.CR2015

Public-key cryptosystem based on invariants of diagonalizable groups

Frantisek Marko, Alexandr N. Zubkov, Martin Juras

We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields…

math.RT2014

The center of $D i s t (G L (m ∣ n))$ in positive characteristic

Alexandr N. Zubkov, Frantisek Marko

The purpose of this paper is to investigate central elements in distribution algebras $D i s t (G)$ of general linear supergroups $G = G L (m ∣ n)$ . As an application, we compute explicitly…

math.MG2014

Routh's theorem for simplices

Frantisek Marko, Semyon Litvinov

It is shown in our earlier paper that, using only tools of elementary geometry, the classical Routh's theorem for triangles can be fully extended to tetrahedra. In this article we…

math.RT2013★ 5 cited

Irreducibility of induced modules for general linear supergroups

Frantisek Marko

In this note we determine when is an induced module H^0_G(λ), corresponding to a dominant integral highest weight λof the general linear supergroup G=GL(m|n) irreducible. Using the…

math.RT2013

Primitive vectors in induced supermodules for general linear supergroups

Frantisek Marko

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 c…

math.RA2011

Pseudocompact algebras and highest weight categories

Frantisek Marko, Alexandr N. Zubkov

We develop a new approach to highest weight categories $C$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi…

math.RT2009

Generators of supersymmetric polynomials in positive characteristic

A. N. Grishkov, F. Marko, A. N. Zubkov

Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie supergalgebra $g l (m ∣ n)$ and a related algebra $A_{s}$ of what they called p…

A combinatorial approach to Donkin-Koppinen filtrations of general linear supergroups

Symmetrizers for Schur superalgebras

A note on the geometry of figurate numbers

Central elements in the distribution algebra of a general linear supergroup and supersymmetric elements

Supersymmetric elements in divided powers algebras

Combinatorial aspects of the linkage principle for general linear supergroups

Minimal degrees of invariants of (super)groups - a connection to cryptology

Linkage principle for ortho-symplectic supergroups

Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebras

Blocks for general linear supergroup GL(m∣n)

Public-key cryptosystem based on invariants of diagonalizable groups

The center of Dist(GL(m∣n)) in positive characteristic

Routh's theorem for simplices

Irreducibility of induced modules for general linear supergroups

Primitive vectors in induced supermodules for general linear supergroups

Pseudocompact algebras and highest weight categories

Generators of supersymmetric polynomials in positive characteristic

Blocks for general linear supergroup $G L (m ∣ n)$

The center of $D i s t (G L (m ∣ n))$ in positive characteristic