Secants of minuscule and cominuscule minimal orbits

Laurent Manivel*, Mateusz Michalek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We study the geometry of the secant and tangential variety of a cominuscule and minuscule variety, e.g. a Grassmannian or a spinor variety. Using methods inspired by statistics we provide an explicit local isomorphism with a product of an affine space with a variety which is the Zariski closure of the image of a map defined by generalized determinants. In particular, equations of the secant or tangential variety correspond to relations among generalized determinants. We also provide a representation theoretic decomposition of cubics in the ideal of the secant variety of any Grassmannian. (C) 2015 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)288-312
Number of pages25
JournalLinear Algebra and Its Applications
Volume481
DOIs
Publication statusPublished - 15 Sep 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Grassmannian
  • Minuscule and cominuscule representation
  • Secant variety
  • Generalized determinant
  • Cumulants
  • TANGENTIAL VARIETIES

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