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- W1495191821 abstract "We initiate a study of the spectral theory of the locally symmetric space $X=Gammabackslash G/K$, where $G=SO(3,Complex)$, $Gamma=SO(3,Z[i])$, $K=SO{3}$. We write down explicit equations defining a fundamental domain for the action of $Gamma$ on $G/K$. The fundamental domain is well-adapted for studying the theory of $Gamma$-invariant functions on $G/K$. We write down equations defining a fundamental domain for the subgroup $Gamma_Z=SO(2,1)_Z$ of $Gamma$ acting on the symmetric space $G_R/K_R$, where $G_R$ is the split real form $SO(2,1)$ of $G$ and $K_R$ is its maximal compact subgroup $SO(2)$. We formulate a simple geometric relation between the fundamental domains of $Gamma$ and $Gamma_Z$ so described. We then use the previous results compute the covolumes of of the lattices $Gamma$ and $Gamma_Z$ in $G$ and $G_R$." @default.
- W1495191821 created "2016-06-24" @default.
- W1495191821 creator A5082296086 @default.
- W1495191821 date "2006-04-29" @default.
- W1495191821 modified "2023-09-27" @default.
- W1495191821 title "A fundamental domain of Ford type for some subgroups of the orthogonal group" @default.
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- W1495191821 hasPublicationYear "2006" @default.
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