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Shadows in Coxeter Groups

Graeber, Marius; Schwer, Petra

Abstract:
For a given w in a Coxeter group W, the elements u smaller than w in Bruhat order can be seen as the end alcoves of stammering galleries of type w in the Coxeter complex Σ. We generalize this notion and consider sets of end alcoves of galleries that are positively folded with respect to certain orientation φ of Σ.We call these sets shadows. Positively folded galleries are closely related to the geometric study of affine Deligne–Lusztig varieties, MV polytopes, Hall–Littlewood polynomials, and many more algebraic structures. In this paper, we will introduce various notions of orientations and hence shadows and study some of their algorithmic properties.

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Verlagsausgabe §
DOI: 10.5445/IR/1000117647
Veröffentlicht am 10.03.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Fakultät für Mathematik (MATH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0218-0006, 0219-3094
KITopen-ID: 1000117647
Erschienen in Annals of combinatorics
Band 24
Seiten 119–147
Vorab online veröffentlicht am 20.02.2020
Nachgewiesen in Web of Science
Scopus
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