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Equivariant multiplicities of Coxeter arrangements and invariant bases
Equivariant multiplicities Coxeter arrangements invariant bases
2010/11/8
Let $\A$ be an irreducible Coxeter arrangement and $W$ be its Coxeter group. Then $W$ naturally acts on $\A$. A multiplicity $\bfm : \A\rightarrow \Z$ is said to be equivariant when $\bfm$ is constant...
A System of Third-Order Differential Operators Conformally Invariant under $\mathfrak{so}(8,\mathbb{C})$
Conformally Invariant math
2010/11/9
In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The...
Invariant Monotone Coupling Need Not Exist
Invariant Monotone Coupling Need Not Exist math
2010/11/15
We show by example that there is a Cayley graph and two invariant random subgraphs $X$ and $Y$ of it such that there exists a monotone coupling between them in the sense that $X \subset Y$ but no suc...
Intersection of stable and unstable manifolds for invariant Morse functions
unstable manifolds invariant Morse functions
2010/11/19
We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.
On the finite-dimensional marginals of shift-invariant measures
On the finite-dimensional marginals shift-invariant measures
2010/11/17
Let $\Sigma$ be a finite alphabet, $\Omega=\Sigma^{\mathbb{Z}^{d}}$ equipped with the shift action, and $\mathcal{I}$ the simplex of shift-invariant measures on $\Omega$. We study the relation betwee...