TY - JOUR

T1 - Second syzygy of determinantal ideals generated by minors of generic symmetric matrices

AU - Hashimoto, Mitsuyasu

PY - 1997/2/14

Y1 - 1997/2/14

N2 - 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.

AB - 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.

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U2 - 10.1016/S0022-4049(96)00004-7

DO - 10.1016/S0022-4049(96)00004-7

M3 - Article

AN - SCOPUS:0031566945

VL - 115

SP - 27

EP - 47

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1

ER -