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A proof of the Popov Conjecture for quivers

โœ Scribed by Geert Van de Weyer

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
193 KB
Volume
274
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Let Q be a quiver with dimension vector ฮฑ. We show that if the space of isomorphism classes of semisimple representations iss(Q, ฮฑ) of Q of dimension vector ฮฑ is not smooth, then the quotient map ฯ€ : rep(Q, ฮฑ) iss(Q, ฮฑ) is not equidimensional. In other words, we prove the Popov Conjecture for the natural action of the linear reductive group GL ฮฑ on the space rep(Q, ฮฑ) of ฮฑ-dimensional representations of the quiver Q.

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