FAVOURABLE MODULES: FILTRATIONS, POLYTOPES, NEWTON–OKOUNKOV BODIES AND FLAT DEGENERATIONS

Evgeny Feigin, Ghislain Fourier, Peter Littelmann

Research output: Contribution to journalArticlepeer-review

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 parametrized by the lattice points of a normal polytope. The filtrations induce at degenerations of the corresponding ag 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.

Original languageEnglish
Pages (from-to)321-352
Number of pages32
JournalTransformation Groups
Volume22
Issue number2
DOIs
StatePublished - 1 Jun 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint

Dive into the research topics of 'FAVOURABLE MODULES: FILTRATIONS, POLYTOPES, NEWTON–OKOUNKOV BODIES AND FLAT DEGENERATIONS'. Together they form a unique fingerprint.

Cite this