2017/10/31 by Pedro de Carvalho Cayres Pinto, Hans-Christian Herbig, Daniel Herden +1 · 4 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Hilbert–Poincaré series #Invariant (physics) #Laurent series #Mathematics #Pure mathematics #SL2(R) #Series (stratigraphy) #math.AC #math.AG #math.RA #msc:05E05 #msc:13A50 #msc:13H10
paper · pdf · doi:10.1142/s0219199719500172
published in Communications in Contemporary Mathematics 22(07), 1950017 (World Scientific) · 33 pages. From v1: added Section 6, minor revisions. From v2: added computations of $γ_2$ and $γ_3$, minor revisions and corrections
openalex created_date 2017/10/20 · arxiv created 2018/06/19 · openalex publication_date 2019/02/26 · arxiv updated 2022/01/19 · openalex updated_date 2026/08/05
Let [Formula: see text] be a finite-dimensional representation of the group [Formula: see text] of [Formula: see text] matrices with complex coefficients and determinant one. Let [Formula: see text] be the algebra of [Formula: see text]-invariant polynomials on [Formula: see text]. We present a calculation of the Hilbert series [Formula: see text] as well as formulas for the first four coefficients of the Laurent expansion of [Formula: see text] at [Formula: see text].