Generalized F-signature of invariant subrings

Abstract

It is known that a certain invariant subring $R$ has finite $F$-representation type. Thus, we can write the $R$-module ${}^{e}R$ as a finite direct sum of finitely many $R$-modules. In such a decomposition of ${}^{e}R$, we pay attention to the multiplicity of each direct summand. For the multiplicity of free direct summand, there is the notion of $F$-signature defined by C. Huneke and G. Leuschke and it characterizes some singularities. In this paper, we extend this notion to non free direct summands and determine the explicit values of them.

9 pages, to appear in J. Algebra, v4:minor changes, v3:added some materials to Section 2 and Section 3, v2: by using the Brauer character, we improved the proof of the main theorem

References in corpus (1)

• F-signature exists

Cited by in corpus (1)

• Dual F-signature of Cohen-Macaulay modules over rational double points