Papers by Gerhard Roehrle
arXiv (Cornell University), Oct 1, 2011
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arXiv (Cornell University), Sep 6, 2012
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arXiv (Cornell University), Mar 25, 2014
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arXiv (Cornell University), Jan 31, 2011
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arXiv (Cornell University), Jan 22, 2018
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arXiv (Cornell University), Mar 27, 2017
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arXiv (Cornell University), Oct 2, 2022
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arXiv (Cornell University), Jan 10, 2012
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arXiv (Cornell University), Apr 20, 2022
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arXiv (Cornell University), May 8, 2017
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arXiv (Cornell University), Oct 5, 2018
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arXiv (Cornell University), May 19, 2023
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arXiv (Cornell University), Nov 23, 2017
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arXiv (Cornell University), Feb 1, 2023
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arXiv (Cornell University), Sep 16, 2014
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arXiv (Cornell University), May 1, 2023
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arXiv (Cornell University), Apr 4, 2011
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arXiv (Cornell University), Mar 3, 2020
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arXiv (Cornell University), May 22, 2009
We consider the finite $W$-algebra $U(\g,e)$ associated to a nilpotent element $e \in \g$ in a si... more We consider the finite $W$-algebra $U(\g,e)$ associated to a nilpotent element $e \in \g$ in a simple complex Lie algebra $\g$ of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a conjecture of Premet, that $U(\g,e)$ always has a 1-dimensional representation, when $\g$ is of type $G_2$, $F_4$, $E_6$ or $E_7$. Thanks to a theorem of Premet, this allows one to deduce the existence of minimal dimension representations of reduced enveloping algebras of modular Lie algebras of the above types. In addition, we deduce that there exists a completely prime primitive ideal in $U(\g)$ whose associated variety is the coadjoint orbit corresponding to $e$.
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arXiv (Cornell University), Jun 29, 2017
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Papers by Gerhard Roehrle