G a M degeneration of flag varieties

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

Let F λ be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module V λ. We define a flat degeneration F λ a variety. Moreover, there exists a larger group G a acting on F λ a, which is a degeneration of the group G. The group G a contains G a M as a normal subgroup. If G is of type A, then the degenerate flag varieties can be embedde'd into the product of Grassmannians and thus to the product of projective spaces. The defining ideal of F λ a is generated by the set of degenerate Plücker relations. We prove that the coordinate ring of F λ a is isomorphic to a direct sum of dual PBW-graded g-modules. We also prove that there exists bases in multi-homogeneous components of the coordinate rings, parametrized by the semistandard PBW-tableux, which are analogs of semistandard tableaux.

Original languageEnglish
Pages (from-to)513-537
Number of pages25
JournalSelecta Mathematica, New Series
Volume18
Issue number3
DOIs
Publication statusPublished - Aug 2012
Externally publishedYes

Keywords

  • Degeneration
  • Flag varieties
  • Lie groups
  • Plücker relations

Fingerprint

Dive into the research topics of 'G a M degeneration of flag varieties'. Together they form a unique fingerprint.

Cite this