Cluster algebras: Notes for the CDM-03 conference

Cluster algebras: Notes for the CDM-03 conference

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by Sergey Fomin , Andrei Zelevinsky

Citations:

12 - 6 self

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@TECHREPORT{Fomin_clusteralgebras:,
    author = {Sergey Fomin and Andrei Zelevinsky},
    title = {Cluster algebras: Notes for the CDM-03 conference},
    institution = {},
    year = {}
}

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Abstract

Abstract. This is an expanded version of the notes of our lectures

Citations

288	On the homotopy associativity of H-spaces - Stasheff
128	Algorithms in Invariant Theory - Sturmfels - 1993
104	On the self-linking of knots - Bott, Taubes - 1994
98	The decorated Teichmüller space of punctured surfaces - Penner - 1987
93	Non-crossing partitions for classical reflection groups, Discrete Math - Reiner - 1997
84	Cluster algebras II: Finite type classification - Fomin, Zelevinsky - 2003
84	Conjectures on the quotient ring by diagonal invariants - Haiman - 1994
75	Cluster algebras I - Fomin, Zelevinsky
74	Double Bruhat cells and total positivity - Fomin, Zelevinsky - 1999
70	Quivers with relations arising from clusters (An case - Caldero, Chapoton, et al. - 2006
60	A.Zelevinsky, Parametrizations of canonical bases and totally positive matrices - Berenstein
56	Total positivity in reductive groups, Lie theory and geometry - Lusztig - 1994
55	Root systems and generalized associahedra - Fomin, Reading - 2005
53	The invariant theory of binary forms - Kung, Rota - 1984
50	Cluster algebras III: Upper bounds and double Bruhat cells - Berenstein, Fomin, et al.
46	A.B.Goncharov, Moduli spaces of local systems and higher Teichmüller theory, arXiv:math/0311149 - Fock
45	Generalized associahedra via quiver representations - Marsh, Reineke, et al.
41	The dual braid monoid, Ann - Bessis
39	Polytopal realizations of generalized associahedra - Chapoton, Fomin, et al.
38	Total positivity in Schubert varieties - Berenstein, Zelevinsky - 1997
34	Ad-nilpotent ideals of a Borel subalgebra - Cellini, Papi
34	A.B.Goncharov: Cluster ensembles, quantization and the dilogarithm, math/0311245 - Fock
34	Total positivity: tests and parametrizations - Fomin, Zelevinsky
32	Positivity and canonical bases in rank 2 cluster algebras of finite and affine types - Sherman, Zelevinsky
27	Cluster algebras and Poisson geometry - Gekhtman, Shapiro, et al. - 2003
23	The Laurent phenomenon, Adv - Fomin, Zelevinsky
23	Vainshtein A.: Cluster algebras and Weil-Petersson forms - Gekhtman, Shapiro
22	Connected components of real double Bruhat cells, Internat - Zelevinsky
19	The cube recurrence - Carroll, Speyer
19	private communication - Thurston - 1991
18	Connected components in the intersection of two open opposite Schubert cells in SLn(R)/B - Shapiro, Shapiro, et al. - 1997
18	The number of ⊕-sign types - Shi - 1997
18	The tropical totally positive grassmannian - Speyer, Williams - 2005
17	Grassmannians and cluster algebras - Scott
13	Explicit presentations for the dual braid monoids - Picantin - 2002
12	From Littlewood-Richardson coefficients to cluster algebras in three lectures, Symmetric Functions 2001: Surveys of Developments and - Zelevinsky - 2002
11	Intersections of Bruhat cells in real flag varieties, IMRN 13 - Rietsch - 1997
11	Skew-symmetric vanishing lattices and intersection of Schubert cells - Shapiro, Shapiro, et al. - 1998
9	The intersection of opposed big cells in real flag varieties, submitted to Proc - Rietsch
9	Recognizing cluster algebras of finite type - Seven
8	Quantum cluster algebras - Berenstein, Zelevinsky
8	Totally nonnegative and oscillatory elements in semisimple groups, preprint math.RT/9811100 - Fomin, Zelevinsky - 1998
8	Simply-laced Coxeter groups and groups generated by symplectic transvections - Shapiro, Shapiro, et al.
6	On conjugacy classes of elements of finite order in compact or complex semisimple Lie groups - Djokovic - 1980
4	Orbits of groups generated by transvections over F2 - Seven
3	The number of connected components in double Bruhat cells for nonsimply-laced groups - Gekhtman, Shapiro, et al.
2	Cluster algebras IV: Classical types, in preparation - Fomin, Zelevinsky
2	algebras: notes for 2004 IMCC (Chonju, Korea, August 2004), preprint math.RT/0407414, (2004) Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet, N7491 - Cluster
1	Tilting theory and cluster - Buan, Marsh, et al.
1	Perfect matchings and the octahedron recurrence, math.CO/ 0402452 - Speyer