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On the number of subrepresentations of a general quiver representation
Author(s) -
Derksen Harm,
Schofield Aidan,
Weyman Jerzy
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm043
Subject(s) - quiver , grassmannian , mathematics , multiplicity (mathematics) , schubert calculus , representation (politics) , intersection (aeronautics) , dimension (graph theory) , pure mathematics , context (archaeology) , combinatorics , algebra over a field , mathematical analysis , geography , cartography , archaeology , politics , political science , law
It is well known that the intersection multiplicities of Schubert classes in the Grassmannian are Littlewood–Richardson coefficients. We generalize this statement in the context of quiver representations. Here the intersection multiplicity of Schubert classes is replaced by the number of subrepresentations of a general quiver representation, and the Littlewood–Richardson coefficients are replaced by the dimension of a certain space of semi‐invariants.