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In this paper, we introduce the notion of combinatorial Aus\-lander-Reiten (AR) quivers for commutation classes $[\widetilde{w}]$ of $w$ in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order $\prec_{[\widetilde{w}]}$ on the subset $\Phi(w)$ of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class $[\widetilde{w}_0]$ of the longest element $w_0$ of any finite type.
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참고문헌 (27)
참고문헌 신청
M. Auslander / 1995 / Representation Theory of Artin Algebras / Cambridge University Press
R. Bedard / 1999 / On commutation classes of reduced words in Weyl groups / European J. Combin 20(6):483~505
N. Bourbaki / 1968 / Actualites Scientifiques et Indus-trielles / Hermann
J. Brundan / 2014 / Homological properties of nite-type Khovanov-Lauda-Rouquier algebras / Duke Math. J 163(7):1353~1404
J. Claxton / 2015 / Young tableaux, multisegments, and PBW bases / Sem. Lothar. Combin 73:21
R. Bedard / 1999 / On commutation classes of reduced words in Weyl groups / European J. Combin 20(6):483~505
N. Bourbaki / 1968 / Actualites Scientifiques et Indus-trielles / Hermann
J. Brundan / 2014 / Homological properties of nite-type Khovanov-Lauda-Rouquier algebras / Duke Math. J 163(7):1353~1404
J. Claxton / 2015 / Young tableaux, multisegments, and PBW bases / Sem. Lothar. Combin 73:21
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