A New Approach To Kazhdan Lusztig Theory Of Type B Via Quantum Symmetric Pairs

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A New Approach To Kazhdan Lusztig Theory Of Type B Via Quantum Symmetric Pairs

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Author : Huanchen Bao
language : en
Publisher:
Release Date : 2018

A New Approach To Kazhdan Lusztig Theory Of Type B Via Quantum Symmetric Pairs written by Huanchen Bao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Hecke algebras categories.

We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satsify a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category [O] of the orthosymplectic Lie superalgebras osp(2m + 1[vertical bar]2n). In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.

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 $A$.

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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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.

Categorical Combinatorial And Geometric Representation Theory And Related Topics

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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-11

Categorical Combinatorial And Geometric Representation Theory And Related Topics written by Pramod N. Achar 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 2024-07-11 with Mathematics categories.

This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.

Hypergeometry Integrability And Lie Theory

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Author : Erik Koelink
language : en
Publisher: American Mathematical Soc.
Release Date : 2022-08-30

Hypergeometry Integrability And Lie Theory written by Erik Koelink 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 2022-08-30 with Education categories.

This volume contains the proceedings of the virtual conference on Hypergeometry, Integrability and Lie Theory, held from December 7–11, 2020, which was dedicated to the 50th birthday of Jasper Stokman. The papers represent recent developments in the areas of representation theory, quantum integrable systems and special functions of hypergeometric type.

Modern Trends In Algebra And Representation Theory

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Author : David Jordan
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17

Modern Trends In Algebra And Representation Theory written by David Jordan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.

Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.

Developments And Retrospectives In Lie Theory

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Author : Geoffrey Mason
language : en
Publisher: Springer
Release Date : 2014-10-31

Developments And Retrospectives In Lie Theory written by Geoffrey Mason and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Mathematics categories.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Semi Infinite Highest Weight Categories

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Author : Jonathan Brundan
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-01

Semi Infinite Highest Weight Categories written by Jonathan Brundan 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 2024-02-01 with Mathematics categories.

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