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Currently displaying 1 – 4 of 4

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On the center of $U_{q} (𝔫^{+})$ . (Sur le centre de $U_{q} (𝔫^{+})$ .)

Caldero, Philippe — 1994

Beiträge zur Algebra und Geometrie

From triangulated categories to cluster algebras II

Philippe Caldero; Bernhard Keller — 2006

Annales scientifiques de l'École Normale Supérieure

Rational smoothness of varieties of representations for quivers of Dynkin type

Philippe Caldero; Ralf Schiffler — 2004

Annales de l’institut Fourier

We study the Zariski closures of orbits of representations of quivers of type $A$ , $D$ ou $E$ . With the help of Lusztig’s canonical base, we characterize the rationally smooth orbit closures and prove in particular that orbit closures are smooth if and only if they are rationally smooth.

The bar automorphism in quantum groups and geometry of quiver representations

Philippe Caldero; Markus Reineke — 2006

Annales de l’institut Fourier

Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the second is in terms of a duality of constructible functions provided by preprojective varieties of quivers.

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