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pro vyhledávání: '"Marko, Frantisek"'
Autor:
Marko, Frantisek, Zubkov, Alexandr N.
We consider the periplectic supergroup ${\bf P} (n)$ over a ground field $\Bbbk$ of characteristic $p>2$. We show that there are four blocks of ${\bf P} (n)$ of simple supermodules $L^{\epsilon}(\lambda)$ corresponding to dominant weights $\lambda$ o
Externí odkaz:
http://arxiv.org/abs/2311.02136
Autor:
Marko, František
We present rational Schur algebra $S(n,r,s)$ over an arbitrary ground field $K$ as a quotient of the distribution algebra $Dist(G)$ of the general linear group $G=GL(n)$ by an ideal $I(n,r,s)$ and provide an explicit description of the generators of
Externí odkaz:
http://arxiv.org/abs/2307.15628
Autor:
Marko, František
We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities descri
Externí odkaz:
http://arxiv.org/abs/2307.15622
Autor:
Marko, František
Publikováno v:
In Journal of Algebra 1 January 2025 661:904-929
Autor:
Marko, Frantisek
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 comput
Externí odkaz:
http://arxiv.org/abs/2008.12239
Autor:
Marko, Frantisek, Zubkov, Alexandr N.
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 $C_{\Gamma}$ is
Externí odkaz:
http://arxiv.org/abs/2008.06558
Autor:
Marko, Frantisek
For the Schur superalgebra $S=S(m|n,r)$ over a ground field $K$ of characteristic zero, we define symmetrizers $T^{\lambda}[i:j]$ of the ordered pairs of tableaux $T_i, T_j$ of the shape $\lambda$ and show that the $K$-span $A_{\lambda,K}$ of all sym
Externí odkaz:
http://arxiv.org/abs/2004.08325
Autor:
Marko, Frantisek
We give a short proof of the formula $n^p=\sum_{\ell=0}^{p-1} (-1)^{\ell} c_{p,\ell} F^{p-\ell}_n$, where $F^{p-\ell}_n$ is the figurate number and $c_{p,\ell}$ is the number of $(p-\ell)$-dimensional facets of $p$-dimensional simplices obtained by c
Externí odkaz:
http://arxiv.org/abs/2004.04678
Autor:
Marko, Frantisek, Zubkov, Alexandr N.
In this paper we investigate the image of the center $Z$ of the distribution algebra $Dist(GL(m|n))$ of the general linear supergroup over a ground field of positive characteristic under the Harish-Chandra morphism $h:Z \to Dist(T)$ obtained by the r
Externí odkaz:
http://arxiv.org/abs/1812.09963
Autor:
Marko, Frantisek
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 supergroup $
Externí odkaz:
http://arxiv.org/abs/1812.09577