Semi-invariants of mixed representations of quivers

A. A. Lopatin; A. N. Zubkov

doi:10.1007/s00031-006-0041-4

Semi-invariants of mixed representations of quivers

A. A. Lopatin, A. N. Zubkov

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

A notion of a mixed representation of a quiver can be derived from ordinary quiver representation by considering the dual action of groups on "vertex" vector spaces together with their usual action. A generating system for the algebra of semi-invariants of mixed representations of a quiver is determined. This is done by reducing the problem to the case of bipartite quivers of a special form and using a function DP on three matrices, which is a mixture of the determinant and two pfaffians.

Original language	English
Pages (from-to)	341-369
Number of pages	29
Journal	Transformation Groups
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s00031-006-0041-4
Publication status	Published - Jun 2007
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s00031-006-0041-4

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AB - A notion of a mixed representation of a quiver can be derived from ordinary quiver representation by considering the dual action of groups on "vertex" vector spaces together with their usual action. A generating system for the algebra of semi-invariants of mixed representations of a quiver is determined. This is done by reducing the problem to the case of bipartite quivers of a special form and using a function DP on three matrices, which is a mixture of the determinant and two pfaffians.

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Semi-invariants of mixed representations of quivers

Abstract

ASJC Scopus subject areas

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