A Soergel-like category for complex reflection groups of rank one
| Autor: | Anne-Laure Thiel, Thomas Gobet |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU) |
| Rok vydání: | 2018 |
| Předmět: |
Hecke algebra
Semisimple algebra Pure mathematics Ring (mathematics) Rank (linear algebra) General Mathematics 010102 general mathematics Free module 01 natural sciences Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics [MATH]Mathematics [math] Representation Theory (math.RT) Reflection group Indecomposable module Mathematics::Representation Theory Complex number Mathematics - Representation Theory ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Mathematische Zeitschrift Mathematische Zeitschrift, Springer, In press, ⟨10.1007/s00209-019-02358-x⟩ |
| ISSN: | 0025-5874 1432-1823 |
| DOI: | 10.48550/arxiv.1812.02284 |
| Popis: | We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators and relations. This ring turns out to be an extension of the Hecke algebra of the reflection group $W$ and a free module of rank $|W| (|W|-1)+1$ over the base ring. We also show that it is a generically semisimple algebra if defined over the complex numbers. Comment: 24 pages. Comments welcome ! |
| Databáze: | OpenAIRE |
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