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Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth [Kõva köide]

(East China Normal Univ, China), (East China Normal Univ, China), (Univ Of New South Wales, Australia)
Teised raamatud teemal:
Teised raamatud teemal:
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.
Portrait of Xihua Cao v
Selected Photos vii
Preface xv
Special Thanks to George Lusztig with Interpretation of Cell Decomposition Picture on the Front Book Cover xxi
Part I Dedications and Reminiscences
1 Professor Xihua Cao and His School
3(6)
Lin Tan
2 Dedications
9(12)
From Henning Haahr Andersen
9(1)
From Vlastimil Dlab
10(1)
From James E. Humphreys
11(1)
From King Fai Lai
11(2)
From Shaoxue Liu
13(4)
From Claus Michael Ringel
17(2)
From Leonard L. Scott, Jr.
19(2)
3 Reminiscences of Family Members
21(8)
My Father Xihua Cao (Shih-hua Tsao)
21(2)
Qunnin Cao
Grandpa and I Will Never Be Apart
23(6)
Xiaoqun Cao
Part II Research Papers
4 A Particular Class of Properly Stratified Algebras
29(10)
Xueqing Chen
Vlastimil Dlab
5 Quantized Cohomological Hall Algebra of the d-Loop Quiver Revisited
39(16)
Neil J. Y. Fan
Changjian Fu
Liangang Peng
6 Generating Algebraic Groups by Small Subgroups and Equivariant Representations
55(20)
Cuipo Jiang
Zongzhu Lin
7 On Quadri-Bialgebras
75(34)
Xiang Ni
Chengming Bai
8 Partial Orderings on Affine Weyl Groups
109(20)
Jianpan Wang
Part III Surveys and Overviews
9 On Toroidal Vertex Algebras
129(16)
Fulin Chen
Shaobin Tan
Qing Wang
Nina Yu
10 A Survey on Infinite-Dimensional Representations of Reductive Algebraic Groups with Frobenius Maps
145(14)
Xiaoyu Chen
Junbin Dong
Nanhua Xi
11 Inductive Conditions of Alperin Weight Conjecture
159(20)
Zhicheng Feng
Jiping Zhang
12 Regular Representations of Quantum Supergroups Uυ(glm\n) and Uυ(qn)
179(34)
Haixia Gu
Zhongguo Zhou
13 BGG Category and Z-Graded Representation Theory
213(28)
Jun Hu
14 Moduli Spaces of Vector Bundles on a Nodal Curve
241(44)
Wenyao Hu
Xiaotao Sun
15 Automorphic Descents
285(30)
Dihua Jiang
16 The Mazur Conjecture, the Lang-Trotter Conjecture and the Hardy-Littlewood Conjecture
315(16)
Hourong Qin
17 A Survey on the Cell Theory of Weighted Coxeter Groups
331(24)
Jianyi Shi
18 On Bases of Quantum Affine Algebras
355(28)
Jie Xiao
Han Xu
Minghui Zhao
Part IV Lecture Notes
19 Lectures on Dualities ABC in Representation Theory
383(66)
Li Luo
Weiqiang Wang
Appendix: A Brief Biography of Xihua Cao 449