Work

Generalized juggling patterns, quiver Grassmannians and affine flag varieties

Year: 2024

Type: article

Abstract: The goal of this paper is to clarify the connection between certain structures from the theory of totally nonnegative Grassmannians, quiver Grassmannians for cyclic quivers and the theory of local models of Shimura varieties. More precisely, we generalize the construction from our previous paper relating the combinatorics and geometry of quiver Grassmannians to that of the totally nonnegative Grassmannians. The varieties we are interested in serve as realizations of local models of Shimura varieties. We exploit quiver representation techniques to study the quiver Grassmannians of interest and, in particular, to describe explicitly embeddings into affine flag varieties which allow us to realize our quiver Grassmannians as a union of Schubert varieties therein.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-024-03614-5

Authors: Evgeny Feigin, Martina Lanini, Alexander Pütz

Institutions: Tel Aviv University, University of Rome Tor Vergata, Paderborn University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Israel Science Foundation, Università degli Studi di Roma Tor Vergata