Second syzygy of determinantal ideals generated by minors of generic symmetric matrices

Mitsuyasu Hashimoto

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Abstract

We prove a characteristic-free plethysm formula of the complex SS2φ for a map of finite free modules φ. We also study a family of subcomplexes of a Schur complex, the v-Schur complexes. Using these machineries from characteristic-free representation theory of general linear group, we give an example of determinantal ideal of generic symmetric matrix whose second Betti number depends on the characteristic of the base field. We also give a short proof of Kurano's first syzygy theorem.

Original languageEnglish
Pages (from-to)27-47
Number of pages21
JournalJournal of Pure and Applied Algebra
Volume115
Issue number1
DOIs
Publication statusPublished - Feb 14 1997

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ASJC Scopus subject areas

  • Algebra and Number Theory

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