Generic Points in Representation Varieties with Applications to Lie Theory and 0-Schur Algebras

Project: Research council

Project Details

Description

Representation theory of quivers (RQT)and Lie theory (LT) are closelyrelated, for instance via root systems.This proposalexplores new connectionsbetween RTQ, LT,quantised enveloping algebras (QEA) and quantised Schur algebras ( QSA).The applicant will first study generic phenomena inrepresentation varieties, in particular, the existence of open orbits, and genericpoints in varieties of pairs of projective representations. Then she will work oninterpreting the generic phenomena in the setting of LT, QEA and QSA.The main applications will be to show the existence of Richardson elementsfor some classes of Lie algebras, in particular for seaweed Lie algebras. Otherapplications include a natural interpretation of combinatorial properties ofroot systems of simple Lie algebras and a new construction of crystal bases.
StatusFinished
Effective start/end date16/01/1215/01/14

Funding

  • Engineering and Physical Sciences Research Council

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  • Research Output

    Projective modules of 0-Schur algebras

    Jensen, B. T., Su, X. & Yang, G., 15 May 2016, In : Journal of Algebra. 454, p. 181-205 25 p.

    Research output: Contribution to journalArticle

  • 2 Citations (Scopus)

    A geometric realisation of 0-Schur and 0-Hecke algebras

    Jensen, B. T. & Su, X., Feb 2015, In : Journal of Pure and Applied Algebra. 219, 2, p. 277-307 31 p.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 3 Citations (Scopus)
    124 Downloads (Pure)

    Adjoint action of automorphism groups on radical endomorphisms, generic equivalence and Dynkin quivers

    Jensen, B. T. & Su, X., 1 Aug 2014, In : Algebras and Representation Theory. 17, 4, p. 1095-1136 42 p.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 1 Citation (Scopus)
    121 Downloads (Pure)