Do the Properties of an S-adic Representation Determine Factor Complexity?
نویسندگان
چکیده
The S-adic conjecture postulates the existence of a condition C such that a sequence has linear complexity if and only if it is an S-adic sequence satisfying C for some finite set S of morphisms. We present an overview of the factor complexity of S-adic sequences and we give some examples that either illustrate some interesting properties, or that are counterexamples to what might seem to be a “good” condition C.
منابع مشابه
Filtrations of smooth principal series and Iwasawa modules
Let $G$ be a reductive $p$-adic group. We consider the general question of whether the reducibility of an induced representation can be detected in a ``co-rank one" situation. For smooth complex representations induced from supercuspidal representations, we show that a sufficient condition is the existence of a subquotient that does not appear as a subrepresentation. An import...
متن کاملTowards a statement of the S-adic conjecture through examples
The S-adic conjecture claims that there exists a condition C such that a sequence has a sub-linear complexity if and only if it is an S-adic sequence satisfying Condition C for some finite set S of morphisms. We present an overview of the factor complexity of S-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could ...
متن کاملGlobally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change, I : Iwasawa algebras and a base change map
This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2, mathbb{Z}_p)$. It then describes a natural base change map between the Iwasawa algebras or more correctly, as it turns out, between the global distribut...
متن کاملDeveloping a BIM-based Spatial Ontology for Semantic Querying of 3D Property Information
With the growing dominance of complex and multi-level urban structures, current cadastral systems, which are often developed based on 2D representations, are not capable of providing unambiguous spatial information about urban properties. Therefore, the concept of 3D cadastre is proposed to support 3D digital representation of land and properties and facilitate the communication of legal owners...
متن کاملL-functions of symmetric powers of the generalized Airy family of exponential sums: l-adic and p-adic methods
For ψ a nontrivial additive character on the finite field Fq, observe that the map t 7→ P x∈Fq ψ(f(x) + tx) is the Fourier transform of the map t 7→ ψ(f(t)). As is well-known, this has a cohomological interpretation, producing a continuous l-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both l-adic and p-adic meth...
متن کامل