Affine Hecke Algebras And Quantum Symmetric Pairs
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Affine Hecke Algebras And Quantum Symmetric Pairs
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Author : Zhaobing Fan
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-18
Affine Hecke Algebras And Quantum Symmetric Pairs written by Zhaobing Fan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-18 with Mathematics categories.
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Affine Flag Varieties And Quantum Symmetric Pairs
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Author : Zhaobing Fan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Affine Flag Varieties And Quantum Symmetric Pairs written by Zhaobing Fan 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 2020-09-28 with Mathematics categories.
The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Twenty Four Hours Of Local Cohomology
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Author : Srikanth B. Iyengar
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-19
Twenty Four Hours Of Local Cohomology written by Srikanth B. Iyengar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-19 with Mathematics categories.
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Forty Years Of Algebraic Groups Algebraic Geometry And Representation Theory In China In Memory Of The Centenary Year Of Xihua Cao S Birth
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Author : Jie Du
language : en
Publisher: World Scientific
Release Date : 2022-10-21
Forty Years Of Algebraic Groups Algebraic Geometry And Representation Theory In China In Memory Of The Centenary Year Of Xihua Cao S Birth written by Jie Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-21 with Mathematics categories.
Professor Xihua Cao (1920-2005) was a leading scholar at East China Normal University (ECNU) and a famous algebraist in China. His contribution to the Chinese academic circle is particularly the formation of a world-renowned 'ECNU School' in algebra, covering research areas include algebraic groups, quantum groups, algebraic geometry, Lie algebra, algebraic number theory, representation theory and other hot fields. In January 2020, in order to commemorate Professor Xihua Cao's centenary birthday, East China Normal University held a three-day academic conference. Scholars at home and abroad gave dedications or delivered lectures in the conference. This volume originates from the memorial conference, collecting the dedications of scholars, reminiscences of family members, and 16 academic articles written based on the lectures in the conference, covering a wide range of research hot topics in algebra. The book shows not only scholars' respect and memory for Professor Xihua Cao, but also the research achievements of Chinese scholars at home and abroad.
Double Affine Hecke Algebras And Congruence Groups
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Author : Bogdan Ion
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
Double Affine Hecke Algebras And Congruence Groups written by Bogdan Ion 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 2021-06-18 with Education categories.
The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by auto-morphisms of a finite index subgroup of the Artin group of type A2, which descends to a faithful outer action of a congruence subgroup of SL(2, Z)or PSL(2, Z). This was previously known only in some special cases and, to the best of our knowledge, not even conjectured to hold in full generality. It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying semisimple data and, to a large extent, even by adjoint data; we prove our main result by reduction to the adjoint case. Adjoint DAAG/DAHA correspond in a natural way to affine Lie algebras, or more precisely to their affinized Weyl groups, which are the semi-direct products W Q∨ of the Weyl group W with the coroot lattice Q∨. They were defined topologically by van der Lek, and independently, algebraically, by Cherednik. We now describe our results for the adjoint case in greater detail. We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type A2,B2,G2 act by automorphisms on the adjoint DAAG/DAHA associated to affine Lie algebras of twist number r =1, 2, 3, respec-tively. This extends a fundamental result of Cherednik for r =1. We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup Γ1(r). In particular, Γ1(r) acts naturally on the set of isomorphism classes of representations of an adjoint DAAG/DAHA of twist number r, giving rise to a projective representation of Γ1(r)on the spaceof aΓ1(r)-stable representation. We also provide a classification of the involutions of Kazhdan-Lusztig type that appear in the context of these actions.
Weight Multiplicities And Young Tableaux Through Affine Crystals
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Author : Jang Soo Kim
language : en
Publisher: American Mathematical Society
Release Date : 2023-03-09
Weight Multiplicities And Young Tableaux Through Affine Crystals written by Jang Soo Kim and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-09 with Mathematics categories.
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Planar Algebras In Braided Tensor Categories
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Author : André Gil Henriques
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-13
Planar Algebras In Braided Tensor Categories written by André Gil Henriques and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.
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Representation Theory Of Geigle Lenzing Complete Intersections
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Author : Martin Herschend
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-23
Representation Theory Of Geigle Lenzing Complete Intersections written by Martin Herschend and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Mathematics categories.
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A Proof That Artificial Neural Networks Overcome The Curse Of Dimensionality In The Numerical Approximation Of Black Scholes Partial Differential Equations
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Author : Philipp Grohs
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07
A Proof That Artificial Neural Networks Overcome The Curse Of Dimensionality In The Numerical Approximation Of Black Scholes Partial Differential Equations written by Philipp Grohs and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.
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Infinite Time Blow Up Solutions To The Energy Critical Wave Maps Equation
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Author : Mohandas Pillai
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07
Infinite Time Blow Up Solutions To The Energy Critical Wave Maps Equation written by Mohandas Pillai and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.
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