Universität zu Köln

Feigin, Evgeny, Fourier, Ghislain and Littelmann, Peter (2017). FAVOURABLE MODULES: FILTRATIONS, POLYTOPES, NEWTON-OKOUNKOV BODIES AND FLAT DEGENERATIONS. Transform. Groups, 22 (2). S. 321 - 353. NEW YORK: SPRINGER BIRKHAUSER. ISSN 1531-586X

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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 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Feigin, Evgeny UNSPECIFIED UNSPECIFIED UNSPECIFIED Fourier, Ghislain UNSPECIFIED UNSPECIFIED UNSPECIFIED Littelmann, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-230404
DOI:	10.1007/s00031-016-9389-2
Journal or Publication Title:	Transform. Groups
Volume:	22
Number:	2
Page Range:	S. 321 - 353
Date:	2017
Publisher:	SPRINGER BIRKHAUSER
Place of Publication:	NEW YORK
ISSN:	1531-586X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TORIC DEGENERATIONS; SCHUBERT VARIETIES; CONTRACTIONS; ALGEBRAS; BASES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/23040