On cohomological Hall algebras of quivers : generators
| Autor: | Olivier Schiffmann, Eric Vasserot |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics 01 natural sciences symbols.namesake High Energy Physics::Theory Mathematics::Quantum Algebra 0103 physical sciences FOS: Mathematics [MATH]Mathematics [math] 0101 mathematics Representation Theory (math.RT) Mathematics::Representation Theory ComputingMilieux_MISCELLANEOUS Mathematics Conjecture Applied Mathematics 010102 general mathematics Quiver Cohomology Nilpotent Hall algebra Poincaré conjecture symbols 010307 mathematical physics Yangian Mathematics - Representation Theory Stack (mathematics) |
| Zdroj: | Journal für die reine und angewandte Mathematik Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2020, 2020 (760), pp.59-132. ⟨10.1515/crelle-2018-0004⟩ |
| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.48550/arxiv.1705.07488 |
| Popis: | We study the cohomological Hall algebra Y of a lagrangian substack of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and their actions on the cohomology of Nakajima quiver varieties. We prove that Y is pure and we compute its Poincare polynomials in terms of (nilpotent) Kac polynomials. We also provide a family of algebra generators. We conjecture that Y is equal, after a suitable extension of scalars, to the Yangian introduced by Maulik and Okounkov. As a corollary, we prove a variant of Okounkov's conjecture, which is a generalization of the Kac conjecture relating the constant term of Kac polynomials to root multiplicities of Kac-Moody algebras. Comment: 69 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|