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- W4294337963 abstract "Let $mathfrak{g}$ be a simple Lie algebra defined over an algebraically closed field $k$ of characteristic $p$. Fix an integer $r>1$ and suppose that $V_1,ldots,V_r$ are irreducible closed subvarieties of $mathfrak{g}$. Let $C(V_1,ldots,V_r)$ be the closed variety of all the pairwise commuting elements in $V_1timescdotstimes V_r$. This paper studies the dimension and irreducibility of such varieties with various $V_i$ in a Lie algebra $mathfrak{g}$. In particular, we complete the problem for the case when $V_i$'s are either $overline{mathcal{O}_{text{sub}}}$ the closure of the subregular orbit or $mathcal{N}$ the nilpotent cone of any rank two Lie algebra $mathfrak{g}$. A result on the dimension of these mixed commuting varieties is generalized for higher ranks. Finally, we apply our calculations to study properties of support varieties for a simple module over the $r$-th Frobenius kernels of $G$." @default.
- W4294337963 created "2022-09-02" @default.
- W4294337963 creator A5079554464 @default.
- W4294337963 date "2013-01-12" @default.
- W4294337963 modified "2023-09-26" @default.
- W4294337963 title "Mixed Commuting Varieties over simple Lie algebras" @default.
- W4294337963 doi "https://doi.org/10.48550/arxiv.1301.2712" @default.
- W4294337963 hasPublicationYear "2013" @default.
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