Feigin, E., Fourier, G. and Littelmann, P. (2017) Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations. Transformation Groups, 22(2), pp. 321-352. (doi: 10.1007/s00031-016-9389-2)
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Abstract
We introduce the notion of a favourable module for a complex unipotent algebraic group, whose properties are governed by the combinatorics of an associated polytope. We describe two filtrations of the module, one given by the total degree on the PBW basis of the corresponding Lie algebra, the other by fixing a homogeneous monomial order on the PBW basis. In the favourable case a basis of the module is parameterized by the lattice points of a normal polytope. The filtrations induce flat degenerations of the corresponding flag variety to its abelianized version and to a toric variety, the special fibres of the degenerations being projectively normal and arithmetically Cohen-Macaulay. The polytope itself can be recovered as a Newton-Okounkov body. We conclude the paper by giving classes of examples for favourable modules.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Fourier, Dr Ghislain |
| Authors: | Feigin, E., Fourier, G., and Littelmann, P. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Transformation Groups |
| Publisher: | Springer Verlag |
| ISSN: | 1083-4362 |
| ISSN (Online): | 1531-586X |
| Published Online: | 02 May 2016 |
| Copyright Holders: | Copyright © 2016 Springer Science+Business Media |
| First Published: | First published in Transformation Groups 22(2):321–352 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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