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

Project: Research council

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

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Schur Algebras
Quantized Enveloping Algebra
Lie Algebra
Crystal Bases
Projective Representation
Simple Lie Algebra
Quiver
Root System
Representation Theory
Orbit