161 research outputs found
Essential connectedness and the rigidity problem for Gaussian symmetrization
We provide a geometric characterization of rigidity of equality cases in
Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is
formulated in terms of a new measure-theoretic notion of connectedness for
Borel sets, inspired by Federer's definition of indecomposable current.Comment: 38 page
Vertices of Lie Modules
Let Lie(n) be the Lie module of the symmetric group S_n over a field F of
characteristic p>0, that is, Lie(n) is the left ideal of FS_n generated by the
Dynkin-Specht-Wever element. We study the problem of parametrizing
non-projective indecomposable summands of Lie(n), via describing their vertices
and sources. Our main result shows that this can be reduced to the case when n
is a power of p. When n=9 and p=3, and when n=8 and p=2, we present a precise
answer. This suggests a possible parametrization for arbitrary prime powers.Comment: 26 page
On the indecomposability of
We study the reverse mathematics of pigeonhole principles for finite powers
of the ordinal . Four natural formulations are presented and their
relative strengths are compared. In the analysis of the pigeonhole principle
for , we uncover two weak variants of Ramsey's Theorem for pairs
Syzygy modules with semidualizing or G-projective summands
Let R be a commutative Noetherian local ring with residue class field k. In
this paper, we mainly investigate direct summands of the syzygy modules of k.
We prove that R is regular if and only if some syzygy module of k has a
semidualizing summand. After that, we consider whether R is Gorenstein if and
only if some syzygy module of k has a G-projective summand.Comment: 13 pages, to appear in Journal of Algebr
Cuspidal representations of sl(n+1)
In this paper we study the subcategory of cuspidal modules of the category of
weight modules over the Lie algebra sl(n+1). Our main result is a complete
classification and explicit description of the indecomposable cuspidal modules.Comment: 31 pages, corrections added, to appear in Adv. Mat
Tree-Automatic Well-Founded Trees
We investigate tree-automatic well-founded trees. Using Delhomme's
decomposition technique for tree-automatic structures, we show that the
(ordinal) rank of a tree-automatic well-founded tree is strictly below
omega^omega. Moreover, we make a step towards proving that the ranks of
tree-automatic well-founded partial orders are bounded by omega^omega^omega: we
prove this bound for what we call upwards linear partial orders. As an
application of our result, we show that the isomorphism problem for
tree-automatic well-founded trees is complete for level Delta^0_{omega^omega}
of the hyperarithmetical hierarchy with respect to Turing-reductions.Comment: Will appear in Logical Methods of Computer Scienc
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