Multivariate Poincaré series for algebras of $S{L}_2$-invariants

Abstract

Let $\mathcal{C}_{\mathbi{d}},$ $\mathcal{I}_{\mathbi{d}},$ $\mathbi{d}{=}(d_1,d_2,..., d_n)$ be the algebras of join covariants and joint invariants of the $n$ binary forms of degrees $d_1,d_2,...,d_n.$ Formulas for computation of the multivariate Poincaré series $\mathcal{P}(\mathcal{C}_{\mathbi{d}},z_1,z_2,...,z_n,t)$ and $\mathcal{P}(\mathcal{I}_{\mathbi{d}},z_1,z_2,...,z_n)$ are found.

arXiv comment5 pages

Cited by in corpus (3)

• Hilbert series associated to symplectic quotients by ${\mathrm{SU}}_2$
• The Hilbert series of ${\mathrm{SL}}_2$-invariants
• Multigraded Hilbert series of invariants, covariants, and symplectic quotients for some rank $1$ Lie groups