Abstract
Several combinatorial actions of the affine Weyl group of type C˜n on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation representations are multiplicity-free. The proof uses a general construction of Gelfand subgroups in the affine Weyl groups of types C˜n and B˜n.
Original language | English |
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Pages (from-to) | 5-33 |
Number of pages | 29 |
Journal | Journal of Algebra |
Volume | 607 |
Early online date | 15 Nov 2021 |
DOIs | |
State | Published - 1 Oct 2022 |
Bibliographical note
Publisher Copyright:© 2021 The Author(s)
Funding
PH was partially supported by Hungarian National Research, Development and Innovation Office ( NKFIH ), Grant No. K115799 , and by a visiting grant from Bar-Ilan University . The project leading to this application has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, Grant agreement No. 741420 . RMA and YR were partially supported by the Israel Science Foundation , Grant No. 1970/18 .
Funders | Funder number |
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Horizon 2020 Framework Programme | |
European Commission | |
Israel Science Foundation | 1970/18 |
Horizon 2020 | 741420 |
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal | K115799 |
Keywords
- Affine Weyl group
- Arc permutation
- Factorisation of the Coxeter element
- Flip
- Gelfand subgroup
- Group action
- Triangulation