On the number of subrepresentations of a general quiver representation

H Derksen; AH Schofield; J Weyman

doi:10.1112/jlms/jdm043

On the number of subrepresentations of a general quiver representation

H Derksen
, AH Schofield
, J Weyman

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

11 Citations (Scopus)

Abstract

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.

Translated title of the contribution	On the number of subrepresentations of a general quiver representation
Original language	English
Pages (from-to)	135 - 147
Number of pages	13
Journal	Journal of the London Mathematical Society
Volume	76 (1)
DOIs	https://doi.org/10.1112/jlms/jdm043
Publication status	Published - Aug 2007

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Publisher: Oxford University Press

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10.1112/jlms/jdm043

http://jlms.oxfordjournals.org/cgi/content/abstract/76/1/135

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title = "On the number of subrepresentations of a general quiver representation",

abstract = "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.",

author = "H Derksen and AH Schofield and J Weyman",

note = "Publisher: Oxford University Press",

year = "2007",

month = aug,

doi = "10.1112/jlms/jdm043",

language = "English",

volume = "76 (1)",

pages = "135 -- 147",

journal = "Journal of the London Mathematical Society",

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T1 - On the number of subrepresentations of a general quiver representation

AU - Derksen, H

AU - Schofield, AH

AU - Weyman, J

N1 - Publisher: Oxford University Press

PY - 2007/8

Y1 - 2007/8

N2 - 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.

AB - 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.

U2 - 10.1112/jlms/jdm043

DO - 10.1112/jlms/jdm043

M3 - Article (Academic Journal)

SN - 1469-7750

VL - 76 (1)

SP - 135

EP - 147

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

ER -

On the number of subrepresentations of a general quiver representation

Abstract

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