Tensor invariants, saturation problems, and Dynkin automorphisms

Jiuzu Hong*, Linhui Shen

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Let G be a connected almost simple algebraic group with a Dynkin automorphism σ. Let Gσ be the connected almost simple algebraic group associated with G and σ. We prove that the dimension of the tensor invariant space of Gσ is equal to the trace of σ on the corresponding tensor invariant space of G. We prove that if G has the saturation property then so does Gσ. As a consequence, we show that the spin group Spin(2n+1) has saturation factor 2, which strengthens the results of Belkale-Kumar [1] and Sam [28] in the case of type Bn.

Original languageEnglish (US)
Pages (from-to)629-657
Number of pages29
JournalAdvances in Mathematics
Volume285
DOIs
StatePublished - Nov 5 2015

Keywords

  • Affine Grassmannian
  • Geometric Satake correspondence
  • Satake basis
  • Saturation problems
  • Tensor multiplicity
  • Tropical points
  • Twining formula

ASJC Scopus subject areas

  • Mathematics(all)

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