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July 2019 Regular prehomogeneous vector spaces for valued Dynkin quivers
Tomohiro Kamiyoshi, Yoshiteru Kurosawa, Hiroshi Nagase, Makoto Nagura
Tsukuba J. Math. 43(1): 71-111 (July 2019). DOI: 10.21099/tkbjm/1571968822

Abstract

We introduce regular prehomogeneous vector spaces associated with an arbitrary valued Dynkin graph $(\Gamma, \boldsymbol{v})$ having a fixed oriented modulation $(𝔐, \Omega)$ over the ground field $K$. Here $K$ is of characteristic zero, but it may not be algebraically closed. We will construct a fundamental theory of such prehomogeneous vector spaces.

Each generic point of a regular prehomogeneous vector space corresponds to a hom-orthogonal partial tilting $\Lambda$-module, where $\Lambda$ is the tensor $K$-algebra of $(𝔐, \Omega)$. We count the number of isomorphism classes of hom-orthogonal partial tilting $\Lambda$-modules of type $\mathbf{B}_n$, $\mathbf{C}_n$, $\mathbf{F}_4$ and $\mathbf{G}_2$. As a consequence of our theorem, we estimate lower and upper bounds for the number of basic relative invariants of regular prehomogeneous vector spaces for any valued Dynkin quiver.

Citation

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Tomohiro Kamiyoshi. Yoshiteru Kurosawa. Hiroshi Nagase. Makoto Nagura. "Regular prehomogeneous vector spaces for valued Dynkin quivers." Tsukuba J. Math. 43 (1) 71 - 111, July 2019. https://doi.org/10.21099/tkbjm/1571968822

Information

Published: July 2019
First available in Project Euclid: 25 October 2019

zbMATH: 07196526
MathSciNet: MR4023315
Digital Object Identifier: 10.21099/tkbjm/1571968822

Subjects:
Primary: 16D80
Secondary: 11S90, 16G20

Rights: Copyright © 2019 University of Tsukuba, Institute of Mathematics

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Vol.43 • No. 1 • July 2019
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