Geometric Complexity Theory Iv Nonstandard Quantum Group For The Kronecker Problem
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Geometric Complexity Theory Iv Nonstandard Quantum Group For The Kronecker Problem
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Author : Jonah Blasiak
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09
Geometric Complexity Theory Iv Nonstandard Quantum Group For The Kronecker Problem written by Jonah Blasiak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.
Recent Developments In Algebraic And Combinatorial Aspects Of Representation Theory
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Author : Vyjayanthi Chari
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-11-25
Recent Developments In Algebraic And Combinatorial Aspects Of Representation Theory written by Vyjayanthi Chari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-25 with Mathematics categories.
This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, USA. It contains original research and survey articles on various topics in the theory of representations of Lie algebras, quantum groups and algebraic groups, including crystal bases, categorification, toroidal algebras and their generalisations, vertex algebras, Hecke algebras, Kazhdan-Lusztig bases, $q$-Schur algebras, and Weyl algebras.
Open Problems In Mathematics
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Author : John Forbes Nash, Jr.
language : en
Publisher: Springer
Release Date : 2016-07-05
Open Problems In Mathematics written by John Forbes Nash, Jr. and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-05 with Mathematics categories.
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.
Irreducible Geometric Subgroups Of Classical Algebraic Groups
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Author : Timothy C. Burness,
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25
Irreducible Geometric Subgroups Of Classical Algebraic Groups written by Timothy C. Burness, and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Geometric group theory categories.
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
Reduced Fusion Systems Over 2 Groups Of Sectional Rank At Most 4
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Author : Bob Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25
Reduced Fusion Systems Over 2 Groups Of Sectional Rank At Most 4 written by Bob Oliver and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Algebraic topology categories.
The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.
Deformation Quantization For Actions Of Kahlerian Lie Groups
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Author : Pierre Bieliavsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
Deformation Quantization For Actions Of Kahlerian Lie Groups written by Pierre Bieliavsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
Let B be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action of B on a Fréchet algebra . Denote by the associated Fréchet algebra of smooth vectors for this action. In the Abelian case BR and isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures R on . When is a -algebra, every deformed Fréchet algebra admits a compatible pre- -structure, hence yielding a deformation theory at the level of -algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.
Irreducible Almost Simple Subgroups Of Classical Algebraic Groups
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Author : Timothy C. Burness
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
Irreducible Almost Simple Subgroups Of Classical Algebraic Groups written by Timothy C. Burness and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.
Level One Algebraic Cusp Forms Of Classical Groups Of Small Rank
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Author : Gaëtan Chenevier
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21
Level One Algebraic Cusp Forms Of Classical Groups Of Small Rank written by Gaëtan Chenevier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Cusp forms (Mathematics) categories.
The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.
On The Differential Structure Of Metric Measure Spaces And Applications
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Author : Nicola Gigli
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
On The Differential Structure Of Metric Measure Spaces And Applications written by Nicola Gigli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.
Multiple Hilbert Transforms Associated With Polynomials
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Author : Joonil Kim
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21
Multiple Hilbert Transforms Associated With Polynomials written by Joonil Kim and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Hilbert transform categories.
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