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arxiv: 1602.01207 · v1 · pith:X66HS5AInew · submitted 2016-02-03 · 🧮 math.RT · math.RA

Kac polynomials for canonical algebras

classification 🧮 math.RT math.RA
keywords algebrascanonicalalgebradimensionfixedpolynomialsproverepresentations
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We prove that the number of geometrically indecomposable representations of fixed dimension vector d of a canonical algebra C defined over a finite field Fq is given by a polynomial in q (depending on C and d). We prove a similar result for squid algebras (and for any almost concealed canonical algebra). Finally we express the volume of the moduli stacks of representations of these algebras of a fixed dimension vector in terms of the corresponding Kac polynomials.

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