Related papers: A note on Iwasawa-type decomposition

We study whether a unital associative algebra $ A $ over a field admits a decomposition of the form $A = Z(A) + [A,A]$ where $ Z(A) $ is the center of $ A $ and $ [A,A] $ denotes the additive subgroup of $A$ generated by all additive…

In this article we generalize results of Clozel and Ray (for $SL_2$ and $SL_n$ respectively) to give explicit ring-theoretic presentation in terms of a complete set of generators and relations of the Iwasawa algebra of the pro-$p$ Iwahori…

It is proved that, if $K$ is a complete discrete valuation field of mixed characteristic $(0,p)$ with residue field satisfying a mild condition, then any abelian variety over $K$ with potentially good reduction has finite…

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…

For any irreducible representation of a surface group into $\mathrm{SL}_2(\mathbb{C})$, we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is…

We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in $R^n$, for $n\ge 3$, with non-empty interiors and of the same measure are equidecomposable using pieces that are measurable.

Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $\theta$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $\theta$ or…

This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Zp-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion…

Let $X$ be a smooth projective variety. We study admissible subcategories of the bounded derived category of coherent sheaves on $X$ whose support is a proper subvariety $Z \subset X$. We show that any one-dimensional irreducible component…

In this article, we study the Iwasawa theory for cuspidal automorphic representations of $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ over CM fields along anticyclotomic directions, in the framework of the Gan--Gross--Prasad conjecture for…

We study Yukawa unification in string models with moduli-dominant SUSY breaking. This type of SUSY breaking in general leads to non-universal soft masses, i.e., soft scalar masses and gaugino masses. Such non-universality is important for…

We construct harmonic maps into SU(1,1)/U(1) starting from Smyth potentials \xi, by the DPW method, In this method, harmonic maps are obtained from the Iwasawa factorization of a solution L of L^{-1} dL = \xi. However, the Iwasawa…

A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $A = BB^T$. We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking interiors of the CP…

Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and…

Consider the general linear group, which is not connected but rather has two connected components, the matrices with positive determinant and the ones with negative determinant. Consider the Iwasawa decomposition of its special linear…

In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…

Considering quantum cosmological minisuperspace models with positive potential, we present evidence that (i) despite common belief there are perspectives for defining a unique, naturally preferred decomposition of the space H of wave…

We show that a compact polyhedron $P$ collapses to a subpolyhedron $Q$ if and only if it admits a piecewise-linear free deformation retraction onto $Q$. We also consider further possibilities for invariant characterisations of…

Let $A$ be an ordinary elliptic curve over a global function field $K$ of characteristic $p$, assumed semistable at every place, and let $L/K$ be a $\mathbb{Z}_p^d$-extension ramified only at finitely many places where $A$ has ordinary…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…