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pro vyhledávání: '"Bendel, Christopher P."'
Let $G$ be a connected reductive group over an algebraically closed field of characteristic $p>0$. Given an indecomposable G-module $M$, one can ask when it remains indecomposable upon restriction to the Frobenius kernel $G_r$, and when its $G_r$-soc
Externí odkaz:
http://arxiv.org/abs/2405.03973
In this paper the authors consider four questions of primary interest for the representation theory of reductive algebraic groups: (i) Donkin's Tilting Module Conjecture, (ii) the Humphreys-Verma Question, (iii) whether $\operatorname{St}_r \otimes L
Externí odkaz:
http://arxiv.org/abs/2209.04675
Autor:
Bendel, Christopher P.
Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The representation theories
Externí odkaz:
http://arxiv.org/abs/2209.01140
Publikováno v:
In Journal of Algebra 1 October 2024 655:95-109
In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl $p$-filtrations for Weyl modules for an algebraic group and Donkin's Tilting Module Conjecture formulated in 1990. New techniqu
Externí odkaz:
http://arxiv.org/abs/2107.11615
Publikováno v:
Representation Theory, 26 (2022), 455-497
In this paper the authors provide a complete answer to Donkin's Tilting Module Conjecture for all rank $2$ semisimple algebraic groups and $\text{SL}_{4}(k)$ where $k$ is an algebraically closed field of characteristic $p>0$. In the process, new tech
Externí odkaz:
http://arxiv.org/abs/2103.14164
In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic $p$ that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin's
Externí odkaz:
http://arxiv.org/abs/1901.06687
Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of prime characteristic $p>0$. Recent work of Kildetoft and Nakano and of Sobaje has shown close connections between two long-standing conjectures of Donkin: one
Externí odkaz:
http://arxiv.org/abs/1804.00613
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Let $G$ be a simple simply connected group scheme defined over ${\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p>0$. Moreover, let $B$ be a Borel subgroup of $G$ and $U$ be the unipotent radical of $B$. In this paper the
Externí odkaz:
http://arxiv.org/abs/1410.2322