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Iyama, Osamu and Jin, Haibo (2023). Positive Fuss-Catalan Numbers and Simple-Minded Systems in Negative Calabi-Yau Categories. Int. Math. Res. Notices, 2023 (8). S. 6624 - 6648. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

We establish a bijection between d-simple-minded systems (d-SMSs) of (-d)-Calabi-Yau cluster category C-d (H) and silting objects of D-b(H) contained in D-<= 0 boolean AND D >= 1-d for hereditary algebra H of Dynkin type and d >= 1. We show that the number of d-SMSs in C-d (H) is the positive Fuss-Catalan number C-d(+)(W) of the corresponding Weyl group W, by applying this bijection and Buan-Reiten-Thomas' and Zhu's results on FominReading's generalized cluster complexes. Our results are based on a refined version of silting-t-structure correspondence.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Iyama, Osamu UNSPECIFIED UNSPECIFIED UNSPECIFIED Jin, Haibo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-674578
DOI:	10.1093/imrn/rnab369
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2023
Number:	8
Page Range:	S. 6624 - 6648
Date:	2023
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TRIANGULATED CATEGORIES; NONCROSSING PARTITIONS; T-STRUCTURES; CONFIGURATIONS; MUTATION; OBJECTS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67457