Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897267 | Journal of Pure and Applied Algebra | 2019 | 25 Pages |
Abstract
Let V be a finite-dimensional representation of the complex circle Cà determined by a weight vector aâZn. We study the Hilbert series Hilba(t) of the graded algebra C[V]Caà of polynomial CÃ-invariants in terms of the weight vector a of the CÃ-action. In particular, we give explicit formulas for Hilba(t) as well as the first four coefficients of the Laurent expansion of Hilba(t) at t=1. The naive formulas for these coefficients have removable singularities when weights pairwise coincide. Identifying these cancelations, the Laurent coefficients are expressed using partial Schur polynomials that are independently symmetric in two sets of variables. We similarly give an explicit formula for the a-invariant of C[V]Caà in the case that this algebra is Gorenstein. As an application, we give methods to identify weight vectors with Gorenstein and non-Gorenstein invariant algebras.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
L. Emily Cowie, Hans-Christian Herbig, Daniel Herden, Christopher Seaton,