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pro vyhledávání: '"20G05, 20J06"'
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
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
Let $G$ be an affine algebraic group scheme over an algebraically closed field $k$ of characteristic $p>0$, and let $G_r$ denote the $r$-th Frobenius kernel of $G$. Motivated by recent work of Friedlander, the authors investigate the class of mock in
Externí odkaz:
http://arxiv.org/abs/1604.03840
Autor:
Boe, Brian D., Bonsignore, Brian, Brons, Theresa, Carlson, Jon F., Chastkofsky, Leonard, Drupieski, Christopher M., Johnson, Niles, Nakano, Daniel K., Li, Wenjing, Luu, Phong Thanh, Macedo, Tiago, Ngo, Nham Vo, Samples, Brandon L., Talian, Andrew J., Townsley, Lisa, Wyser, Benjamin J.
Publikováno v:
J. Algebra 360 (2012), 21-52
Let $G$ be a simple, simply-connected algebraic group defined over $\mathbb{F}_p$. Given a power $q = p^r$ of $p$, let $G(\mathbb{F}_q) \subset G$ be the subgroup of $\mathbb{F}_q$-rational points. Let $L(\lambda)$ be the simple rational $G$-module o
Externí odkaz:
http://arxiv.org/abs/1110.0228
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0211a535c6f70acb8d97500a7266c436
http://arxiv.org/abs/1804.00613
http://arxiv.org/abs/1804.00613
Let $G$ be an affine algebraic group scheme over an algebraically closed field $k$ of characteristic $p>0$, and let $G_r$ denote the $r$-th Frobenius kernel of $G$. Motivated by recent work of Friedlander, the authors investigate the class of mock in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f216b7f9882fd7e8196872aea926259