Quivers, invariants and quotient correspondence

Yi Hu, Sangjib Kim

Research output: Contribution to journalArticle

Abstract

This paper studies the geometric and algebraic aspects of the moduli spaces of quivers of fence type. We first provide two quotient presentations of the quiver varieties and interpret their equivalence as a generalized Gelfand-MacPherson correspondence. Next, we introduce parabolic quivers and extend the above from the actions of reductive groups to the actions of parabolic subgroups. Interestingly, the above geometry finds its natural counterparts in the representation theory as the branching rules and transfer principle in the context of the reciprocity algebra. The last half of the paper establishes this connection.

Original languageEnglish (US)
Pages (from-to)197-216
Number of pages20
JournalJournal of Algebra
Volume393
DOIs
StatePublished - Nov 1 2013

Fingerprint

Quiver
Quotient
Correspondence
Invariant
Branching Rules
Parabolic Subgroup
Reductive Group
Reciprocity
Representation Theory
Moduli Space
Equivalence
Algebra

Keywords

  • Branching rules
  • GIT quotients
  • Quotient correspondences
  • Representation theory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Quivers, invariants and quotient correspondence. / Hu, Yi; Kim, Sangjib.

In: Journal of Algebra, Vol. 393, 01.11.2013, p. 197-216.

Research output: Contribution to journalArticle

Hu, Yi ; Kim, Sangjib. / Quivers, invariants and quotient correspondence. In: Journal of Algebra. 2013 ; Vol. 393. pp. 197-216.
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