Affine Flag Varieties And Quantum Symmetric Pairs
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Affine Flag Varieties and Quantum Symmetric Pairs
Author: Zhaobing Fan
language: en
Publisher: American Mathematical Soc.
Release Date: 2020-09-28
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
Author: Zhaobing Fan
language: en
Publisher: American Mathematical Society
Release Date: 2023-01-18
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Twenty-Four Hours of Local Cohomology
Author: Srikanth B. Iyengar
language: en
Publisher: American Mathematical Society
Release Date: 2022-07-19
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.