08651nam 22006133 450 991095996160332120221222215054.097814704713471470471345(MiAaPQ)EBC29731896(Au-PeEL)EBL29731896(CKB)24767184200041(OCoLC)1343249351(RPAM)22685292(EXLCZ)992476718420004120220627d2022 uy 0engurcn|||||||||txtrdacontentcrdamediacrrdacarrierHypergeometry, integrability and lie theory Virtual Conference on Hypergeometry, Integrability and Lie Theory, December 7-11, 2020, Lorentz Center, Leiden, Netherlands /Erik Koelink, Stefan Kolb, Nicolai Reshetikhin, Bart Vlaar, editors1st ed.Providence, Rhode Island :American Mathematical Society,[2022]1 online resource (xii, 347 pages) illustrationsContemporary mathematics,0271-4132 ;volume 780Print version: Koelink, Erik Hypergeometry, Integrability and Lie Theory Providence : American Mathematical Society,c2022 9781470465209 Includes bibliographical references.Cover -- Title page -- Contents -- Preface -- 1. Sectionformat {Background}{1} -- 2. Sectionformat {Structure of workshop}{1} -- 3. Sectionformat {A special occasion}{1} -- Characteristic functions of -adic integral operators -- 1. Introduction -- 2. Zeta-functions -- 3. Realization of _{ , , } on analytic functions -- 4. -hypergeometric functions and proof of Theorem 1.1 -- 5. Examples -- 6. The non-homogeneous case -- Acknowledgments -- References -- Shuffle algebras, lattice paths and the commuting scheme -- 1. Introduction -- 2. Hecke algebra and lattice paths -- 3. The shuffle algebra -- 4. Matching the partition functions with shuffle elements -- 5. Application to the commuting scheme -- Acknowledgments -- References -- The bar involution for quantum symmetric pairs -hidden in plain sight -- 1. Introduction -- 2. Preliminaries -- 3. The quasi -matrix, revisited -- 4. The bar involution for quantum symmetric pairs, revisited -- References -- Charting the -Askey scheme -- 1. Introduction -- 2. Askey-Wilson polynomials and Verde-Star's theorem -- 3. The -Verde-Star scheme -- 4. The -Verde-Star scheme as a four-manifold -- 5. Further perspectives -- Appendix A. Explicit data for the families in Figure 1 -- Appendix B. Some explicit limit transitions -- Acknowledgement -- References -- Filtered deformations of elliptic algebras -- 1. Introduction -- 2. Filtered deformations -- 3. Resolutions of elliptic algebras -- 4. Elliptic noncommutative del Pezzo surfaces -- 5. Filtered deformations from del Pezzo surfaces -- 6. Classifications -- Acknowledgments -- References -- Pseudo-symmetric pairs for Kac-Moody algebras -- 1. Introduction -- 1.1. Pseudo-involutions and pseudo-fixed-point subalgebras -- 1.2. Applications in the quantum deformed setting -- 1.3. Outline -- 2. Pseudo-involutions in terms of compatible decorations.2.1. Generalized Cartan matrices and Dynkin diagrams -- 2.2. Braid group and Weyl group -- 2.3. Minimal realization and bilinear forms -- 2.4. Kac-Moody algebra and roots -- 2.5. Kac-Moody group and triple exponentials -- 2.6. Subdiagrams of finite type -- 2.7. Automorphisms of -- 2.8. Twisted involutions and compatible decorations -- 2.9. Classification of pseudo-involutions of the second kind -- 3. Pseudo-fixed-point subalgebras in terms of generalized Satake diagrams -- 3.1. The subalgebra -- 3.2. Generalized Satake diagrams -- 3.3. Basic properties of -- 3.4. Iwasawa decomposition for pseudo-symmetric pairs -- 3.5. A combinatorial description of ' -- 4. The restricted Weyl group and restricted root system -- 4.1. The ℚ-span of the root system -- 4.2. Root system involutions and the corresponding orthogonal decompositions -- 4.3. The restricted root system -- 4.4. Combinatorial bases for ^{ } and ^{- }. -- 4.5. The Weyl group of the restricted root system -- 4.6. The group ^{ } and the restricted Weyl group \overline -- 4.7. A combinatorial prescription of the simple restricted reflections: the group ̃ -- 4.8. The group (\overlineΦ) revisited -- 4.9. The restricted Weyl group as a Coxeter group -- 4.10. Non-reduced and non-crystallographic root systems -- Appendix A. Classification of generalized Satake diagrams -- A.1. Notation -- A.2. Low-rank coincidences -- A.3. Finite type -- A.4. Affine type -- Acknowledgments -- References -- Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains -- 1. Introduction -- 2. -Point spherical functions -- 3. Structure theory of real semisimple Lie groups -- 4. Generalised radial component maps -- 5. The quantum Calogero-Moser spin chain -- 6. The asymptotic boundary KZB operators -- 7. Example: ( , ). -- Acknowledgment -- References.Elementary symmetric polynomials and martingales for Heckman-Opdam processes -- 1. Introduction -- 2. Heckman-Opdam theory -- 3. The compact case of type _{ -1} -- 4. The non-compact case of type _{ -1} -- 5. The non-compact case of type _{ } -- References -- Conformal hypergeometry and integrability -- 1. Introduction -- 2. Conformal field theory and partial waves -- 3. Conformal partial waves and hypergeometry -- 4. Integrability of multipoint conformal partial waves -- 5. Concluding comments -- Acknowledgment -- References -- Determinant of _{ }-hypergeometric solutions under ample reduction -- 1. Introduction -- 2. KZ equations -- 3. Coefficients of polynomials -- 4. _{ }-Beta integral and KZ equations for =2 -- 5. Leading term of a polynomial solution -- 6. Leading term of an _{ }-hypergeometric solution -- 7. Determinant of _{ }-hypergeometric solutions -- 8. Properties of _{ }-hypergeometric solutions -- Acknowledgment -- References -- Notes on solutions of KZ equations modulo ^{ } and -adic limit ∞ -- 1. Introduction -- 2. KZ equations -- 3. Complex solutions -- 4. Solutions modulo ^{ } -- 5. Independence of modules from the choice of -- 6. Filtrations and homomorphisms -- 7. Coefficients of solutions -- 8. Multiplication by and Cartier-Manin matrix -- 9. Change of variables -- 10. -Adic convergence -- Appendix A. The case =3 and Dwork's theory -- Acknowledgments -- References -- Back Cover.Characteristic functions of p-adic integral operators / Pavel Etingof and David Kazhdan -- Shuffle algebras, lattice paths and the commuting scheme / Alexandr Garbali and Paul Zinn-Justin -- The bar involution for quantum symmetric pairs -- hidden in plain sight / Stefan Kolb -- Charting the q-Askey scheme / Tom Koornwinder -- Filtered deformations of elliptic algebras / Eric M. Rains -- Pseudo-symmetric pairs for Kac-Moody algebras / Vidas Regelskis and Bart Vlaar -- Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains / Nicolai Reshetikhin and Jasper Stokman -- Elementary symmetric polynomials and martingales for Heckman-Opdam processes / Margit Rösler and Michael Voit -- Conformal hypergeometry and integrability / Volker Schomerus -- Determinant of Fp-hypergeometric solutions under ample reduction / Alexander Varchenko -- Notes on solutions of KZ equations modulo ps and p-adic limits (with an appendix by Steven Sperber and Alexander Varchenko) / Alexander Varchenko.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.Contemporary mathematics (American Mathematical Society) ;v. 780.Hypergeometric functionsCongressesIntegral geometryCongressesLie groupsCongressesHypergeometric functionsIntegral geometryLie groups515/.55515.5513A3516S3817B3717B6717B8033C6033C6733D4543A9060J60mscKoelink Hendrik1964-Kolb Stefan1971-Reshetikhin NicolaiVlaar Bart1979-MiAaPQMiAaPQMiAaPQBOOK9910959961603321Hypergeometry, integrability and lie theory4346311UNINA