Brandon Samples - University of Georgia VIGRE Algebra Group

Brandon Samples
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Brandon Samples
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University of Georgia VIGRE Algebra Group
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Mathematics - Representation Theory (2)
 
Mathematics - Group Theory (2)
 
Mathematics - Number Theory (1)

Publications Authored By Brandon Samples

2011Oct
Affiliations: 1University of Georgia VIGRE Algebra Group, 2University of Georgia VIGRE Algebra Group, 3University of Georgia VIGRE Algebra Group, 4University of Georgia VIGRE Algebra Group, 5University of Georgia VIGRE Algebra Group, 6University of Georgia VIGRE Algebra Group, 7University of Georgia VIGRE Algebra Group, 8University of Georgia VIGRE Algebra Group, 9University of Georgia VIGRE Algebra Group, 10University of Georgia VIGRE Algebra Group, 11University of Georgia VIGRE Algebra Group, 12University of Georgia VIGRE Algebra Group, 13University of Georgia VIGRE Algebra Group, 14University of Georgia VIGRE Algebra Group, 15University of Georgia VIGRE Algebra Group, 16University of Georgia VIGRE Algebra Group

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 of highest weight $\lambda$. Read More

2010Oct
Affiliations: 1University of Georgia VIGRE Algebra Group, 2University of Georgia VIGRE Algebra Group, 3University of Georgia VIGRE Algebra Group, 4University of Georgia VIGRE Algebra Group, 5University of Georgia VIGRE Algebra Group, 6University of Georgia VIGRE Algebra Group, 7University of Georgia VIGRE Algebra Group, 8University of Georgia VIGRE Algebra Group, 9University of Georgia VIGRE Algebra Group, 10University of Georgia VIGRE Algebra Group, 11University of Georgia VIGRE Algebra Group, 12University of Georgia VIGRE Algebra Group, 13University of Georgia VIGRE Algebra Group, 14University of Georgia VIGRE Algebra Group, 15University of Georgia VIGRE Algebra Group

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\mathbb{F}_p$. Given $r \geq 1$, set $q=p^r$, and let $G(\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\mathbb{F}_q),L(\lambda))$ where $L(\lambda)$ is the simple $G$-module of highest weight $\lambda$. Read More

We consider a generalization of the Frobenius Problem where the object of interest is the greatest integer which has exactly $j$ representations by a collection of positive relatively prime integers. We prove an analogue of a theorem of Brauer and Shockley and show how it can be used for computation. Read More