STABLE HILBERT SERIES OF S(g)K FOR CLASSICAL GROUPS
نویسنده
چکیده
Given a classical symmetric pair, (G, K), with g = Lie(G), we provide descriptions of the Hilbert series of the algebra of K-invariant vectors in the associated graded algebra of U(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) → ∞.
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