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Principal subspaces for the quantum affine vertex algebra in type A1(1) |
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| Affiliation: | 1. Department of Mathematics, University of Rijeka, Radmile Matej?i? 2, 51000 Rijeka, Croatia;2. Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;1. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Campus Gragoatá, Rua Alexandre Moura 8 - São Domingos, 24210-200 Niterói, Rio de Janeiro, Brazil;2. Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli 30, 44121 Ferrara, Italy;1. Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia;2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia;3. Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia;4. Department of Mathematics, University of Oviedo, Calvo Sotelo, s/n, 33007 Oviedo, Spain;5. Department of Mathematics, Federal University of Ceará, Pici Campus, Block 914, 60455-760, Fortaleza, Brazil;6. Department of Mathematics, University of São Paulo, Butantã, 05508-090, São Paulo, Brazil;1. Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Morelia, Michoacán, 58089, Mexico;2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Cd. Universitaria, Colonia Copilco el Bajo, Alcaldía Coyoacán, 04510, México D.F., Mexico;1. Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia;2. Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia;3. School of Computing, Engineering and Mathematics, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia;1. IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune, 411008, India;2. Fachgruppe Mathematik/Informatik, Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany |
| Abstract: | By using the ideas of Feigin and Stoyanovsky and Calinescu, Lepowsky and Milas we introduce and study the principal subspaces associated with the Etingof–Kazhdan quantum affine vertex algebra of integer level and type . We show that the principal subspaces possess the quantum vertex algebra structure, which turns to the usual vertex algebra structure of the principal subspaces of generalized Verma and standard modules at the classical limit. Moreover, we find their topological quasi-particle bases which correspond to the sum sides of certain Rogers–Ramanujan-type identities. |
| Keywords: | Quantum vertex algebra Principal subspace Combinatorial bases |
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