2018/09/20 by Hans-Christian Herbig, Daniel Herden, Christopher Seaton · 6 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Mathematics #Pure mathematics #Quotient #Series (stratigraphy) #Symplectic geometry #math.AC #math.RA #math.SG #msc:05E05 #msc:13A50 #msc:14L30 #msc:53D20
paper · pdf · doi:10.1142/s0218196720500435
published in International Journal of Algebra and Computation 30(07), 1323-1357 (World Scientific) · 23 pages, 3 figures, 1 table
arxiv created 2018/09/20 · openalex publication_date 2020/07/24 · openalex created_date 2020/07/29 · arxiv updated 2022/01/19 · openalex updated_date 2026/07/28
We compute the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an [Formula: see text]-module and give an explicit expression for the first nonzero coefficient of the Laurent expansion of the Hilbert series at [Formula: see text]. Our expression for the Hilbert series indicates an algorithm to compute it, and we give the output of this algorithm for all representations of dimension at most [Formula: see text]. Along the way, we compute the Hilbert series of the module of covariants of an arbitrary [Formula: see text]- or [Formula: see text]-module as well as its first three Laurent coefficients.