Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes


Journal Article

This note constructs the flat toric degeneration of the manifold ℱℓn of flags in ℂn due to Gonciulea and Lakshmibai (Transform. Groups 1(3) (1996) 215) as an explicit GIT quotient of the Gröbner degeneration due to Knutson and Miller (Gröbner geometry of Schubert polynomials, Ann. Math. (2) to appear). This implies that Schubert varieties degenerate to reduced unions of toric varieties, associated to faces indexed by rc-graphs (reduced pipe dreams) in the Gelfand-Tsetlin polytope. Our explicit description of the toric degeneration of ℱℓn provides a simple explanation of how Gelfand-Tsetlin decompositions for irreducible polynomial representations of GLn arise via geometric quantization. © 2004 Elsevier Inc. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Kogan, M; Miller, E

Published Date

  • May 1, 2005

Published In

Volume / Issue

  • 193 / 1

Start / End Page

  • 1 - 17

International Standard Serial Number (ISSN)

  • 0001-8708

Digital Object Identifier (DOI)

  • 10.1016/j.aim.2004.03.017

Citation Source

  • Scopus