The Grassmannian Gr(k,n) admits an action by a finite cyclic group of order n via the cyclic shift automorphism. The combinatorial structures underlying both total nonnegativity and clusters for Gr(k,n) are cyclically equivariant, which is one explanation for the particular elegance of these structures in the case of Gr(k,n). We will explore the L-shift locus in Gr(k,n), i.e. the subvariety of points fixed by the Lth power of the cyclic shift. Steven Karp recently showed that the 1-shift locus consists of finitely many points. On the other hand the n-shift locus is Gr(k,n) itself. Our theorems interpolate between these extremes: we provide a simple geometric description of the L-shift locus for any L, describe its total nonnegativity locus as a stratified space, and propose an atlas of generalized cluster charts (in the style of Chekhov-Shapiro) whose clusters are total positivity tests.
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08
mai
Vendredi
Chris Fraser (Minnesota): Cyclic symmetry loci in Grassmannians
08 mai 2020, 11:00
- 08 mai 2020, 12:00
En ligne/online,
Canada
Détails
Date :
mai 8, 2020
Heure :
11:00 am - 12:00 pm
Lieu
Venue Name:
En ligne/online
Address:
Canada