Universität zu Köln

Fang, Xiu, Fourier, Ghislain and Littelmann, Peter (2017). Essential bases and toric degenerations arising from birational sequences. Adv. Math., 312. S. 107 - 150. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2082

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Abstract

We present a new approach to construct T-equivariant flat toric degenerations of flag varieties and spherical varieties, combining ideas coming from the theory of Newton Okounkov bodies with ideas originally stemming from PBW-filtrations. For each pair (S,>) consisting of a birational sequence and a monomial order, we attach to the affine variety G//U a monoid Gamma = Gamma(S, >). As a side effect we get a vector space basis is B-Gamma of C[G//U], the elements being indexed by Gamma. The basis B-Gamma has multiplicative properties very similar to those of the dual canonical basis. This makes it possible to transfer the methods of Alexeev and Brion [1] to this more general setting, once one knows that the monoid Gamma is finitely generated and saturated. (C) 2017 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Fang, Xiu UNSPECIFIED UNSPECIFIED UNSPECIFIED Fourier, Ghislain UNSPECIFIED UNSPECIFIED UNSPECIFIED Littelmann, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-230708
DOI:	10.1016/j.aim.2017.03.014
Journal or Publication Title:	Adv. Math.
Volume:	312
Page Range:	S. 107 - 150
Date:	2017
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2082
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 NEWTON-OKOUNKOV BODIES; CANONICAL BASES; PBW FILTRATION; CRYSTAL BASES; VARIETIES; MODULES; A(N) Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/23070