Linear maps preserving invariants
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- by Gerald W. Schwarz PDF
- Proc. Amer. Math. Soc. 136 (2008), 4197-4200 Request permission
Abstract:
Let $G\subset \mathrm {GL}(V)$ be a complex reductive group. Let $G’$ denote $\{\varphi \in \mathrm {GL}(V)\mid p\circ \varphi =p\text { for all }p\in \mathbb {C}[V]^G\}$. We show that, “in general”, $G’=G$. In case $G$ is the adjoint group of a simple Lie algebra $\mathfrak {g}$, we show that $G’$ is an order 2 extension of $G$. We also calculate $G’$ for all representations of $\mathrm {SL}_2$.References
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Additional Information
- Gerald W. Schwarz
- Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454-9110
- MR Author ID: 157450
- Email: schwarz@brandeis.edu
- Received by editor(s): November 14, 2007
- Published electronically: July 23, 2008
- Additional Notes: This work was partially supported by NSA Grant H98230-06-1-0023
- Communicated by: Gail R. Letzter
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 4197-4200
- MSC (2000): Primary 20G20, 22E46, 22E60
- DOI: https://doi.org/10.1090/S0002-9939-08-09628-7
- MathSciNet review: 2431032