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Genz, Volker, Koshevoy, Gleb and Schumann, Bea (2020). Polyhedral parametrizations of canonical bases & cluster duality. Adv. Math., 369. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2082

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Abstract

We establish the relation of Berenstein-Kazhdan's decoration function and Gross-Hacking-Keel-Kontsevich's potential on the open double Bruhat cell in the base affine space G/N of a simple, simply connected, simply laced algebraic group G. As a byproduct we derive explicit identifications of polyhedral parametrization of canonical bases of the ring of regular functions on G/N arising from the tropicalizations of the potential and decoration function with the classical string and Lusztig parametrizations. In the appendix we construct maximal green sequences for the open double Bruhat cell in G/N which is a crucial assumption for Gross- Hacking-Keel-Kontsevich's construction. (C) 2020 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Genz, Volker UNSPECIFIED UNSPECIFIED UNSPECIFIED Koshevoy, Gleb UNSPECIFIED UNSPECIFIED UNSPECIFIED Schumann, Bea UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-323918
DOI:	10.1016/j.aim.2020.107178
Journal or Publication Title:	Adv. Math.
Volume:	369
Date:	2020
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2082
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TORIC DEGENERATIONS; FLAG Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/32391