MULTITRANSITIVITY OF CALOGERO-MOSER SPACES
| Autor: | Alimjon Eshmatov, Farkhod Eshmatov, Yuri Berest |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Transitive relation Algebra and Number Theory 010102 general mathematics Diagonal Automorphism 01 natural sciences Combinatorics Unimodular matrix 0103 physical sciences Ordered pair 010307 mathematical physics Geometry and Topology Configuration space 0101 mathematics Mathematics |
| Zdroj: | Transformation Groups. 21:35-50 |
| ISSN: | 1531-586X 1083-4362 |
| DOI: | 10.1007/s00031-015-9332-y |
| Popis: | Let G be the group of unimodular automorphisms of a free associative ℂ-algebra on two generators. A theorem of G. Wilson and the first author [BW] asserts that the natural action of G on the Calogero-Moser spaces Cn is transitive for all n ϵ ℕ. We extend this result in two ways: first, we prove that the action of G on Cn is doubly transitive, meaning that G acts transitively on the configuration space of ordered pairs of distinct points in Cn; second, we prove that the diagonal action of G on \( {C}_{n_1}\times {C}_{n_2}\times \cdots \times {C}_{n_m} \) is transitive provided n1, n2, …, nm are pairwise distinct numbers. |
| Databáze: | OpenAIRE |
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