Quiver-graded Richardson orbits

Eiriksson Ö, Sauter J (2019)
COMMUNICATIONS IN ALGEBRA.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Abstract / Bemerkung
In Lie theory, a dense orbit in the nilpotent radical of a parabolic group under the operation of the parabolic is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalizing the classical definition in the case of the general linear group. We define a quasi-hereditary algebra called the nilpotent quiver algebra whose isomorphism classes of Delta-filtered modules correspond to orbits in our generalized setting. We translate the existence of a Richardson orbit into the existence of a rigid Delta-filtered module of a given dimension vector. We study an idempotent recollement of this algebra whose associated intermediate extension functor can be used to produce Richardson orbits in some situations. This can be explicitly calculated in examples. We also give examples where no Richardson orbit exists.
Stichworte
Quiver Grassmannian; representation variety; quasi-hereditary algebra; recollement
Erscheinungsjahr
2019
Zeitschriftentitel
COMMUNICATIONS IN ALGEBRA
ISSN
0092-7872
eISSN
1532-4125
Page URI
https://pub.uni-bielefeld.de/record/2935583

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Eiriksson Ö, Sauter J. Quiver-graded Richardson orbits. COMMUNICATIONS IN ALGEBRA. 2019.
Eiriksson, Ö., & Sauter, J. (2019). Quiver-graded Richardson orbits. COMMUNICATIONS IN ALGEBRA. doi:10.1080/00927872.2019.1588974
Eiriksson, Ö., and Sauter, J. (2019). Quiver-graded Richardson orbits. COMMUNICATIONS IN ALGEBRA.
Eiriksson, Ö., & Sauter, J., 2019. Quiver-graded Richardson orbits. COMMUNICATIONS IN ALGEBRA.
Ö. Eiriksson and J. Sauter, “Quiver-graded Richardson orbits”, COMMUNICATIONS IN ALGEBRA, 2019.
Eiriksson, Ö., Sauter, J.: Quiver-graded Richardson orbits. COMMUNICATIONS IN ALGEBRA. (2019).
Eiriksson, Ögmundur, and Sauter, Julia. “Quiver-graded Richardson orbits”. COMMUNICATIONS IN ALGEBRA (2019).