Affine Flag Varieties and Quantum Symmetric Pairs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Affine Flag Varieties and Quantum Symmetric Pairs write by Zhaobing Fan. This book was released on 2020-09-28. Affine Flag Varieties and Quantum Symmetric Pairs available in PDF, EPUB and Kindle. 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
Affine Hecke Algebras and Quantum Symmetric Pairs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Affine Hecke Algebras and Quantum Symmetric Pairs write by Zhaobing Fan. This book was released on 2023-01-18. Affine Hecke Algebras and Quantum Symmetric Pairs available in PDF, EPUB and Kindle. View the abstract.
Twenty-Four Hours of Local Cohomology
Twenty-Four Hours of Local Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Twenty-Four Hours of Local Cohomology write by Srikanth B. Iyengar. This book was released on 2022-07-19. Twenty-Four Hours of Local Cohomology available in PDF, EPUB and Kindle. 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.
Double Affine Hecke Algebras and Congruence Groups
Double Affine Hecke Algebras and Congruence Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Double Affine Hecke Algebras and Congruence Groups write by Bogdan Ion. This book was released on 2021-06-18. Double Affine Hecke Algebras and Congruence Groups available in PDF, EPUB and Kindle. 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.
Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties
Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties write by Hiroshi Iritani. This book was released on 2021-06-21. Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties available in PDF, EPUB and Kindle. Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.
