Hypergeometry, 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, editors

• Record Nr.: UNINA9910959961603321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2022]
• ISBN: 9781470471347; 1470471345
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (xii, 347 pages) : illustrations
• Collana: Contemporary mathematics, , 0271-4132 ; ; volume 780
• Classificazione: 13A3516S3817B3717B6717B8033C6033C6733D4543A9060J60
• Disciplina: 515/.55; 515.55
• Soggetti: Hypergeometric functions; Integral geometry; Lie groups
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.