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CANONICAL DECOMPOSITION AND QUIVER REPRESENTATIONS OF TYPE $\tilde {A}_n$ OVER FINITE FIELDS

Part of: Representation theory of rings and algebras

Published online by Cambridge University Press:  22 September 2022

QINGHUA CHEN Open the ORCID record for QINGHUA CHEN [Opens in a new window]  and
YE LIU Open the ORCID record for YE LIU [Opens in a new window]
QINGHUA CHEN*
Affiliation:
School of Mathematics and Statistics, Fu Zhou University, Fu Zhou, Fujian 350108, PR China
YE LIU
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China Current address: The high school attached to Hunan Normal University, Chang Sha, Hunan 410006, PR China e-mail: 252241859@qq.com
*
e-mail: 252241859@qq.com
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Abstract

Let Q be a quiver of type $\tilde {A}_n$ . Let $\alpha =\alpha _1+\alpha _2+\cdots +\alpha _s$ be the canonical decomposition. For the polynomials $M_Q(\alpha ,q)$ that count the number of isoclasses of representations of Q over ${\mathbb F}_q$ with dimension vector $\alpha $ , we obtain a precise relation between the degree of $M_Q(\alpha ,q)$ and that of $\prod _{i=1}^{s} M_Q(\alpha _i,q)$ for an arbitrary dimension vector $\alpha $ .

Keywords

canonical decompositionquiver representationdimension vector

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 250 - 260
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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