Generalized associahedra via quiver representations

Authors:
Robert Marsh, Markus Reineke and Andrei Zelevinsky

Journal:
Trans. Amer. Math. Soc. **355** (2003), 4171-4186

MSC (2000):
Primary 52B11, 16G20, 17B20; Secondary 17B37, 05E99

DOI:
https://doi.org/10.1090/S0002-9947-03-03320-8

Published electronically:
June 10, 2003

MathSciNet review:
1990581

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties of these fans then become easy consequences of the known facts about tilting modules due to K. Bongartz, D. Happel and C. M. Ringel.

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Additional Information

**Robert Marsh**

Affiliation:
Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, England

Email:
R.Marsh@mcs.le.ac.uk

**Markus Reineke**

Affiliation:
BUGH Wuppertal, Gaußstraße 20, D-42097 Wuppertal, Germany

Email:
reineke@math.uni-wuppertal.de

**Andrei Zelevinsky**

Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Email:
andrei@neu.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03320-8

Received by editor(s):
May 26, 2002

Received by editor(s) in revised form:
February 8, 2003

Published electronically:
June 10, 2003

Additional Notes:
Andrei Zelevinsky’s research was supported in part by NSF grants #DMS-9971362 and DMS-0200299. Robert Marsh’s research was supported in part by EPSRC grant GR/R17546/01. All authors were supported in part by a University of Leicester Research Fund Grant

Article copyright:
© Copyright 2003
by Robert Marsh, Markus Reineke, and Andrei Zelevinsky