Related papers: Distinguished Regular Supercuspidal Representation…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
To understand cognitive reasoning in the brain, it has been proposed that symbols and compositions of symbols are represented by activity patterns (vectors) in a large population of neurons. Formal models implementing this idea [Plate…
A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite…
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…
Deep supervised learning has achieved great success in the last decade. However, its deficiencies of dependence on manual labels and vulnerability to attacks have driven people to explore a better solution. As an alternative,…
Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework…
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…
Let F be a non-archimedean local field of odd residual characteristic. Let G be a (connected) reductive group over F that splits over a tamely ramified field extension of F. We revisit Yu's construction of smooth complex representations of…
We compute the characters of simple supercuspidal representations of twisted GL(2n) and standard SO(2n+1) over a p-adic field. Comparing them by the endoscopic character relation, we determine the liftings of simple supercuspidal…
These notes provide three contributions to the (well-established) representation theory of Dynkin and Euclidean quivers. They should be helpful as part of a direct approach to study representations of quivers, and they may shed some new…
This paper aims to clarify the representational status of Deep Learning Models (DLMs). While commonly referred to as 'representations', what this entails is ambiguous due to a conflation of functional and relational conceptions of…
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Let U(N) be the quasi-split unitary group in N variables for a quadratic unramified extension of p-adic fields. We compute the characters of simple supercuspidal representations of twisted GL(N) and U(N). Comparing them by the endoscopic…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
Representation learning is the foundation of machine reading comprehension and inference. In state-of-the-art models, character-level representations have been broadly adopted to alleviate the problem of effectively representing rare or…
We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…
We show that, in good residual characteristic, most supercuspidal representations of a tamely ramified reductive p-adic group G arise from pairs (S,\theta), where S is a tame elliptic maximal torus of G, and \theta is a character of S…
The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…