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Idempotent (Asymptotic) Mathematics and the Representation Theory [PDF]
, 2002 A brief introduction to Idempotent Mathematics is presented. Idempotent Mathematics can be treated as a result of a dequantization of the traditional Mathematics as the Planck constant tends to zero taking pure imaginary values.
G. Litvinov, V. Maslov, G. Shpiz
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Integral motivic sheaves and geometric representation theory [PDF]
Advances in Mathematics, 2022 With representation-theoretic applications in mind, we construct a formalism of reduced motives with integral coefficients. These are motivic sheaves from which the higher motivic cohomology of the base scheme has been removed.
J. Eberhardt, Jakob Scholbach
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The Representation Theory of Neural Networks [PDF]
Mathematics, 2020 In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical object that we ...
M. Armenta, Pierre-Marc Jodoin
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Integral representation theory
Graduate Texts in Mathematics, 2021 In this chapter, we consider a slightly more general framework on the preceding chapters: we consider lattices as projective modules, and relate this to invertibility and representation theory in an integral sense.
J. Voight
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Cotorsion torsion triples and the representation theory of filtered hierarchical clustering [PDF]
Advances in Mathematics, 2019 We give a full classification of representation types of the subcategories of representations of an m × n rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two ...
Ulrich Bauer +3 more
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Complex Semisimple Quantum Groups and Representation Theory [PDF]
Lecture notes in mathematics, 2017 This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups.
Christian Voigt, R. Yuncken
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STABILITY PATTERNS IN REPRESENTATION THEORY [PDF]
Forum of Mathematics, Sigma, 2013 We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories.
Steven V. Sam, Andrew Snowden
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Tilting Theory: A Gift of Representation Theory to Mathematics [PDF]
The Mathematical Intelligencer, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Introduction to representation theory [PDF]
Graduate Studies in Mathematics, 2009 Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and ...
Pavel Etingof +6 more
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