Secants of minuscule and cominuscule minimal orbits

Research output: Contribution to journalArticleScientificpeer-review

Details

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

Researchers

Research units

  • Max Planck Inst Math Sci, Max Planck Society
  • Polish Acad Sci, Polish Academy of Sciences, Math Inst
  • Aix Marseille Universite

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.

    Research areas

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

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