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Semi-invariants of mixed representations of quivers

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Pevtsova Street 13, Omsk 644099, Russia

    A.A. Lopatin

  2. Chair of Geometry, Omsk State Pedagogical University, Tuhachevskogo Embankment 14, Omsk 644099, Russia

    A.N. Zubkov

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  1. A.A. Lopatin
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  2. A.N. Zubkov
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Correspondence to A.A. Lopatin or A.N. Zubkov.

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Lopatin, A., Zubkov, A. Semi-invariants of mixed representations of quivers. Transformation Groups 12, 341–369 (2007). https://doi.org/10.1007/s00031-006-0041-4

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  • DOI: https://doi.org/10.1007/s00031-006-0041-4

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