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Certain Polynomial Functions on N
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a e E(P,A a e P,A adJoint representation analytic associated graded assume asymptotic basis element C-function C-ring Choose Clearly coefficients compact subsets compute convergent Corollary 8.2 decomposition difference equations dimensional double unitary representation exists a constant extends filtered ring finite finite-dimensional follows form a basis Furthermore graded ring Hence i|i e induction inJective integral domain invariant irreducible isomorphism leading term Lemma Lie algebra linear mapping M-module structure M,tm maximal parabolic subgroup meromorphic function module homomorphism monomials multiplication non-zero parabolic pair parabolic subgroup polynomial function Proof Proposition 3.1 reduced degree Remark root vectors satisfy conditions semi-lattice Similarly submodules subspace suffices to show Suppose that b e Theorem Theory uniformly for m e unique unitary representation universal enveloping algebra valid vector space Y2 Yl Y2 Yl Y2 Yl