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arXiv · 1809.07760

Hilbert series associated to symplectic quotients by $\operatorname{SU}_2$

Hans-Christian Herbig·Daniel Herden·Christopher Seaton
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Abstract

We compute the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an $\operatorname{SU}_2$-module and give an explicit expression for the first nonzero coefficient of the Laurent expansion of the Hilbert series at $t = 1$. Our expression for the Hilbert series indicates an algorithm to compute it, and we give the output of this algorithm for representations of dimension at most $10$. Along the way, we compute the Hilbert series of the module of covariants of an arbitrary $\operatorname{Sl}_2$- or $\operatorname{SU}_2$-module as well its first three Laurent coefficients.

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BibTeXRIS

Hans-Christian Herbig, Daniel Herden, Christopher Seaton. 2018-09-20. Hilbert series associated to symplectic quotients by $\operatorname{SU}_2$. https://doi.org/10.1142/s0218196720500435

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