On Schubert varieties of complexity one

Let $B$ be a Borel subgroup of ${GL}_{n} (ℂ)$ and $𝕋$ a maximal torus contained in $B$ . Then $𝕋$ acts on ${GL}_{n} (ℂ) ∕ B$ and every Schubert variety is $𝕋$ -invariant. We say that a Schubert variety is of complexity $k$ if a maximal $𝕋$ -orbit in $X_{w}$ has codimension $k$ . We discuss topology, geometry, and combinatorics related to Schubert varieties of complexity one.

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Keywords

Schubert varieties, torus action, pattern avoidance, flag Bott–Samelson varieties, flag Bott manifolds

Mathematical Subject Classification

Primary: 14M15, 14M25

Secondary: 05A05

Milestones

Received: 8 October 2020

Revised: 16 July 2021

Accepted: 11 October 2021

Published: 19 January 2022

Authors

Eunjeong Lee
Center for Geometry and Physics Institute for Basic Science (IBS) Pohang South Korea

Mikiya Masuda
Department of Mathematics Osaka City University Osaka Japan

Seonjeong Park
Department of Mathematics Education Jeonju University Jeonju South Korea

Vol. 315, No. 2, 2021

Eunjeong Lee, Mikiya Masuda and Seonjeong Park

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors