Stable Hilbert series of $\mathcal S(\mathfrak g)^K$ for classical groups

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dc.creatorWillenbring, Jeb F.
dc.date2005-10-29
dc.date2005-11-06
dc.date.accessioned2026-07-07T06:48:06Z
dc.date.available2026-07-07T06:48:06Z
dc.descriptionGiven a classical symmetric pair, $(G,K)$, with $\mathfrak g = Lie(G)$, we provide descriptions of the Hilbert series of the algebra of $K$-invariant vectors in the associated graded algebra of $\mathcal U(\mathfrak g)$ viewed as a $K$-representation under restriction of the adjoint representation. The description illuminates a certain stable behavior of the Hilbert series, which is investigated in a case-by-case basis. We note that the stable Hilbert series of one symmetric pair often coincides with others. Also, for the case of the real form $U(p,q)$ we derive a closed expression for the Hilbert series when $\min(p,q) \to \infty$.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0510649
dc.identifierhttp://arxiv.org/abs/math/0510649
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103874
dc.subjectRepresentation Theory
dc.titleStable Hilbert series of $\mathcal S(\mathfrak g)^K$ for classical groups
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