%0 Journal Article %1 ISI:000380382100011 %A Bellamy, Gwyn %A Thiel, Ulrich %C 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA %D 2016 %I ACADEMIC PRESS INC ELSEVIER SCIENCE %J JOURNAL OF ALGEBRA %K Calogero-Moser Cherednik Hecke Symplectic algebras; groups; leaves} reflection spaces; {Complex %P 197-252 %R 10.1016/j.jalgebra.2016.06.003 %T Cuspidal Calogero-Moser and Lusztig families for Coxeter groups %V 462 %X The goal of this paper is to compute the cuspidal Calogero-Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by first computing the symplectic leaves of the associated Calogero-Moser space and then by classifying certain ``rigid'' modules. Numerical evidence suggests that there is a very close relationship between Calogero-Moser families and Lusztig families. Our classification shows that, additionally, the cuspidal Calogero-Moser families equal cuspidal Lusztig families for the infinite families of Coxeter groups. (C) 2016 Elsevier Inc. All rights reserved.

@article{ISI:000380382100011, abstract = {{The goal of this paper is to compute the cuspidal Calogero-Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by first computing the symplectic leaves of the associated Calogero-Moser space and then by classifying certain ``rigid{''} modules. Numerical evidence suggests that there is a very close relationship between Calogero-Moser families and Lusztig families. Our classification shows that, additionally, the cuspidal Calogero-Moser families equal cuspidal Lusztig families for the infinite families of Coxeter groups. (C) 2016 Elsevier Inc. All rights reserved.}}, added-at = {2017-05-18T11:32:12.000+0200}, address = {{525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA}}, affiliation = {{Thiel, U (Reprint Author), Univ Stuttgart, Fachbereich Math, Inst Algebra \& Zahlentheorie, Lehrstuhl Algebra, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Bellamy, Gwyn, Univ Glasgow, Sch Math \& Stat, Glasgow G12 8QW, Lanark, Scotland. Thiel, Ulrich, Univ Stuttgart, Fachbereich Math, Inst Algebra \& Zahlentheorie, Lehrstuhl Algebra, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}}, author = {Bellamy, Gwyn and Thiel, Ulrich}, author-email = {{gwyn.bellamy@glasgow.ac.uk thiel@mathematik.uni-stuttgart.de}}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2f23cd11b9935b57e1537e6427907985c/hermann}, doi = {{10.1016/j.jalgebra.2016.06.003}}, eissn = {{1090-266X}}, funding-acknowledgement = {{DFG Schwerpunktprogramm {[}1489]}}, funding-text = {{The authors would like to thank Cedric Bonnafe and Meinolf Geck for many fruitful discussions. We also thank Dan Ciubotaru for informing us about his preprint {[}14] and his result that for E<INF>7</INF> the cuspidal Lusztig family does not contain rigid modules. Moreover, we would like to thank Gunter Malle for commenting on a preliminary version of this article. The second author was partially supported by the DFG Schwerpunktprogramm 1489.}}, interhash = {1e2bb6cf3e8e1fec0bf054d279d08f66}, intrahash = {f23cd11b9935b57e1537e6427907985c}, issn = {{0021-8693}}, journal = {{JOURNAL OF ALGEBRA}}, keywords = {Calogero-Moser Cherednik Hecke Symplectic algebras; groups; leaves} reflection spaces; {Complex}, keywords-plus = {{RATIONAL CHEREDNIK ALGEBRAS; SYMPLECTIC REFLECTION ALGEBRAS; HECKE ALGEBRAS; PARTITION; SUBGROUPS; SPACE; G(M; N)}}, language = {{English}}, month = {{SEP 15}}, number-of-cited-references = {{43}}, orcid-numbers = {{Bellamy, Gwyn/0000-0002-7045-4177}}, pages = {{197-252}}, publisher = {{ACADEMIC PRESS INC ELSEVIER SCIENCE}}, research-areas = {{Mathematics}}, researcherid-numbers = {{Bellamy, Gwyn/C-4966-2014}}, times-cited = {{0}}, timestamp = {2017-05-18T09:32:12.000+0200}, title = {{Cuspidal Calogero-Moser and Lusztig families for Coxeter groups}}, type = {{Article}}, volume = {{462}}, web-of-science-categories = {{Mathematics}}, year = {{2016}} }