Related papers: Applications of Crystal Bases to Current Problems …
We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.
Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
In July 2012 the General Assembly of the United Nations resolved that 2014 should be the International Year of Crystallography, 100 years since the award of the Nobel Prize for the discovery of X-ray diffraction by crystals. On this special…
Let X=G/K be a Riemannian symmetric space of the noncompact type. We give a short exposition of the representation theory related to X, and discuss its holomorphic extension to the complex crown, a G-invariant subdomain in the complexified…
These exercises complement my notes "Derived categories, resolutions, and Brown representability".
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…
In the paper "Confinement of matroid representations to subsets of partial fields" (arXiv:0806.4487) we introduced the Hydra-k partial fields to study quinary matroids with inequivalent representations. The proofs of some results on these…
We develop the notion of crystal in the context of derived algebraic geometry, and to connect crystals to more classical objects such as D-modules.
In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak q(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak q(n))$-modules in the category…
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
The Takagi-Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations…
The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems.
Despite its centrality in the philosophy of cognitive science, there has been little prior philosophical work engaging with the notion of representation in contemporary NLP practice. This paper attempts to fill that lacuna: drawing on ideas…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with periodic boundary conditions, for which the Brillouin zone is a…